Determining if an Image is Real or Virtual

  • 1.

    A can is placed {eq}20\ \rm cm {/eq} in front of a convex lens whose focal length is equal to {eq}30\ \rm cm {/eq}. Determine the image distance and the nature of the image formed by the lens.

    Answers:

    • The image distance is {eq}12\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}60\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}60\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}12\ \rm cm {/eq} and the image formed is a virtual image.

  • 2.

    The image produced by a convex lens is equal to {eq}v {/eq}. If an object is kept {eq}25\ \rm cm {/eq} in front of the lens whose focal length is equal to {eq}10\ \rm cm {/eq}, find the image distance and determine whether the image produced is real or virtual.

    Answers:

    • The image distance is {eq}16.67\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}6.14\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}6.14\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}16.67\ \rm cm {/eq} and the image formed is a virtual image.

  • 3.

    Calculate the image distance and the nature of the image formed when an object is placed {eq}15\ \rm cm {/eq} in front of a converging lens of a focal length of {eq}20\ \rm cm {/eq}.

    Answers:

    • The image distance is {eq}60.0\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}85.7\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}85.7\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}60.0\ \rm cm {/eq} and the image formed is a virtual image.

  • 4.

    Determine the image distance and the type of the image formed when an object is kept at a distance of {eq}45\ \rm cm {/eq} from a concave lens whose focal length is equal to {eq}18\ \rm cm {/eq}.

    Answers:

    • A real image is formed at a distance of {eq}45.86\ \rm cm {/eq}.

    • A virtual image is formed at a distance of {eq}12.86\ \rm cm {/eq}

    • A real image is formed at a distance of {eq}12.86\ \rm cm {/eq}.

    • A virtual image is formed at a distance of {eq}45.86\ \rm cm {/eq}.

  • 5.

    An object of height {eq}10.0\ \rm cm {/eq} is placed {eq}25.0\ \rm cm {/eq} in front of a convex lens whose focal length is {eq}10.0\ \rm cm {/eq}. Calculate the image distance and determine what kind of image, real or virtual, will be formed for this arrangement.

    Answers:

    • The image distance is {eq}16.7\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}7.1\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}7.1\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}16.7\ \rm cm {/eq} and the image formed is a real image.

  • 6.

    An object is located at a distance of {eq}36\ \rm cm {/eq} from a converging lens whose focal length is {eq}10\ \rm cm {/eq}. Determine the image distance and whether the image formed is real or virtual.

    Answers:

    • The image distance is {eq}13.8\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}13.8\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}7.8\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}7.8\ \rm cm {/eq} and the image formed is a real image.

  • 7.

    An image is formed by a convex lens with a focal length of {eq}3.2\ \rm cm {/eq} when an object is located at a distance of {eq}4.0\ \rm cm {/eq} from the lens. Determine the image distance and if the image real or virtual.

    Answers:

    • The image distance is {eq}1.8\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}16.0\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}1.8\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}16.0\ \rm cm {/eq} and the image formed is a virtual image.

  • 8.

    Sara places a scientific calculator in front of a concave lens whose focal length is equal to {eq}15\ \rm cm {/eq}. If the calculator is placed at a distance of {eq}18\ \rm cm {/eq} away from the lens, determine what kind of image is observed by Sara.

    Answers:

    • Virtual image and it is located approximately {eq}8.18\ \rm cm {/eq} away from the lens.

    • Real image and it is located approximately {eq}18.18\ \rm cm {/eq} away from the lens.

    • Real image and it is located approximately {eq}8.18\ \rm cm {/eq} away from the lens.

    • Virtual image and it is located approximately {eq}18.18\ \rm cm {/eq} away from the lens.

  • 9.

    Find the image distance and the type of image formed by a concave lens using the data given below.

    Object distance, {eq}u=32\ \rm cm {/eq}

    Focal length, {eq}f=20\ \rm cm {/eq}.

    Answers:

    • Virtual and the image distance is equal to {eq}12.3\ \rm cm {/eq}.

    • A real and upright image is formed and is located at a distance of {eq}12.3\ \rm cm {/eq} from the lens.

    • Real and the image distance is equal to {eq}12.3\ \rm cm {/eq}.

    • A virtual and inverted image is formed and is located at a distance of {eq}12.3\ \rm cm {/eq} from the lens.

  • 10.

    The focal length of a convex lens is {eq}40\ \rm cm {/eq} and an object is placed at a distance of {eq}50\ \rm cm {/eq} in front of it. Calculate the image distance and determine if the image is real or virtual.

    Answers:

    • The image distance is {eq}22.2\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}22.2\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}200.0\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}200.0\ \rm cm {/eq} and the image formed is a real image.

  • 11.

    Kate places an object at a distance of {eq}17\ \rm cm {/eq} from a convex lens. Determine the image distance and find whether the image formed is real or virtual if the lens has a focal length of {eq}7.97\ \rm cm {/eq}.

    Answers:

    • The image distance is {eq}15\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}18\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}18\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}15\ \rm cm {/eq} and the image formed is a virtual image.

  • 12.

    A box is placed in front of a concave lens of focal length {eq}20\ \rm cm {/eq}. If the box is placed at a distance of {eq}35\ \rm cm {/eq} away from the lens, determine whether the image of the box produced is real or virtual.

    Answers:

    • Real because the lens is diverging.

    • Virtual because the lens is diverging.

    • Virtual because the lens is converging.

    • Real because the lens is converging.

  • 13.

    Determine the image distance and determine whether the image formed is real or virtual when a cylinder is placed {eq}51\ \rm cm {/eq} in front of a converging lens of a focal length of {eq}35\ \rm cm {/eq}.

    Answers:

    • A virtual image is formed at a distance of {eq}111.56\ \rm cm {/eq}.

    • A real image is formed at a distance of {eq}111.56\ \rm cm {/eq}.

    • A real image is formed at a distance of {eq}20.86\ \rm cm {/eq}.

    • A virtual image is formed at a distance of {eq}20.86\ \rm cm {/eq}.

  • 14.

    An image is formed on the same side as that of the object when it is placed {eq}15\ \rm cm {/eq} in front of a diverging lens of a focal length of {eq}10\ \rm cm {/eq}. Calculate the image distance and determine whether the image produced is real or virtual.

    Answers:

    • The image distance is {eq}30.0\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}30.0\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}6.0\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}6.0\ \rm cm {/eq} and the image formed is a virtual image.

  • 15.

    The distance between a diverging lens and an object is {eq}38\ \rm cm {/eq}. Calculate the image distance and determine whether the image formed is real or virtual if the focal length of the lens is {eq}65\ \rm cm {/eq}.

    Answers:

    • The image distance is {eq}24.0\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}91.5\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}24.0\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}91.5\ \rm cm {/eq} and the image formed is a virtual image.

  • 16.

    An object is placed at a distance of {eq}38\ \rm cm {/eq} from a converging lens, whose focal distance is equal to {eq}15\ \rm cm {/eq}. Calculate the image distance and determine if the image formed is real or virtual.

    Answers:

    • The image distance is {eq}10.8\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}24.8\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}10.8\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}24.8\ \rm cm {/eq} and the image formed is a virtual image.

  • 17.

    An image is formed by a convex lens with a focal length of {eq}65.2\ \rm cm {/eq} when an object is kept at a distance of {eq}120\ \rm cm {/eq} from the lens. Calculate the image distance and determine if the image is real or virtual.

    Answers:

    • The image distance is {eq}142.8\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}142.8\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}42.2\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}42.2\ \rm cm {/eq} and the image formed is a virtual image.

  • 18.

    The object distance and the focal length of a diverging lens are {eq}22\ \rm cm {/eq} and {eq}35\ \rm cm {/eq}, respectively. Which of the following options corresponds to the type of image formed due to this configuration?

    Answers:

    • The image distance is {eq}13.5\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}59.2\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}159.2\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}13.5\ \rm cm {/eq} and the image formed is a real image.

  • 19.

    Calculate the image distance and determine the type of image, real or virtual, formed when an object is placed {eq}18\ \rm cm {/eq} in front of a concave lens of a focal length of {eq}37\ \rm cm {/eq}.

    Answers:

    • The image distance is {eq}35.1\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}12.1\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}35.1\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}12.1\ \rm cm {/eq} and the image formed is a virtual image.

  • 20.

    What kind of image will be formed, real or virtual, when the object distance is {eq}80\ \rm cm {/eq} for an object placed at the center of the curvature of a convex lens with a focal length of {eq}40\ \rm cm {/eq}.

    Answers:

    • The image distance is {eq}26.7\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}26.7\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}80.0\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}80.0\ \rm cm {/eq} and the image formed is a virtual image.

  • 21.

    An object is placed at a distance of {eq}80\ \rm cm {/eq} from a convex lens whose focal length is {eq}50\ \rm cm {/eq}. Calculate the image distance and determine whether the image formed is real or virtual.

    Answers:

    • The image distance is {eq}133.3\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}30.8\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}133.3\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}30.8\ \rm cm {/eq} and the image formed is a real image.

  • 22.

    A diverging lens of a focal length of {eq}44\ \rm cm {/eq} produces an image of an object placed {eq}36\ \rm cm {/eq} in front of the lens. Calculate the image distance and determine if the image is real or virtual.

    Answers:

    • The image distance is {eq}19.8\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}2.0\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}19.8\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}2.0\ \rm cm {/eq} and the image formed is a virtual image.

  • 23.

    Calculate the image distance and determine whether the image formed by a converging lens is real or virtual when an object is placed {eq}45\ \rm cm {/eq} in front of the lens whose focal length is {eq}90\ \rm cm {/eq}.

    Answers:

    • The image distance is {eq}30.0\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}90.0\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}30.0\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}90.0\ \rm cm {/eq} and the image formed is a real image.

  • 24.

    A converging lens has a focal length of {eq}32\ \rm cm {/eq}. If an object is placed at a distance of {eq}16\ \rm cm {/eq} from the lens, calculate the image distance and determine what kind of image will be formed, real or virtual.

    Answers:

    • The image distance is {eq}32.0\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}10.7\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}32.0\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}10.7\ \rm cm {/eq} and the image formed is a real image.

  • 25.

    The distance between a diverging lens and a candle is {eq}23\ \rm cm {/eq}. Calculate the image distance and determine the kind of image that will be formed, real or virtual, if the focal length of the lens is also equal to {eq}23\ \rm cm {/eq}.

    Answers:

    • The image distance is {eq}11.5\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}23.0\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}11.5\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}23.0\ \rm cm {/eq} and the image formed is a real image.

  • 26.

    An image is formed when an object is placed {eq}15\ \rm cm {/eq} in front of a concave lens. If the focal length of the lens is equal to {eq}25\ \rm cm {/eq}, calculate the image distance and determine whether the image formed is real or virtual.

    Answers:

    • The image distance is {eq}9.4\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}37.5\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}37.5\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}9.4\ \rm cm {/eq} and the image formed is a virtual image.

  • 27.

    An object is placed at a distance of {eq}61.71\ \rm cm {/eq} from a convex lens whose focal length is {eq}27\ \rm cm {/eq}. Calculate the image distance and determine the type of image formed, real or virtual.

    Answers:

    • The image distance is {eq}48.0\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}18.8\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}18.8\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}48.0\ \rm cm {/eq} and the image formed is a virtual image.

  • 28.

    The object distance and the focal length of a converging lens are given below. Using the lens formula, calculate the image distance and determine whether the image formed will be real or virtual.

    {eq}d_o=40\ \rm cm {/eq}

    {eq}f=20\ \rm cm {/eq}

    Answers:

    • The image distance is {eq}13.3\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}40.0\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}40.0\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}13.3\ \rm cm {/eq} and the image formed is a real image.

  • 29.

    Calculate the image distance and determine the type of image formed by a concave lens whose focal length is {eq}27\ \rm cm {/eq} and the object is placed at a distance of {eq}42\ \rm cm {/eq} in front of the lens.

    Answers:

    • The image distance is {eq}16.4\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}75.6\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}75.6\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}16.4\ \rm cm {/eq} and the image formed is a virtual image.

  • 30.

    During an observation, it is found that the focal length of a convex lens is {eq}29\ \rm cm {/eq}. Calculate the image distance and determine whether the image is real or virtual if the object distance is {eq}14\ \rm cm {/eq}.

    Answers:

    • The image distance is {eq}27.1\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}9.4\ \rm cm {/eq} and the image formed is a real image.

    • The image distance is {eq}27.1\ \rm cm {/eq} and the image formed is a virtual image.

    • The image distance is {eq}9.4\ \rm cm {/eq} and the image formed is a virtual image.

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