Using a Ray Tracing Diagram & the Lens Equation to Find the Image Produced by Two Identical Lenses

  • 1.

    Which of the following is the correct option for the image formed by lens 2 as shown in the figure:

    Answers:

    • {eq}\text{The final image is upright, real, and equal to the original object.} {/eq}

    • {eq}\text{The final image is inverted, real, and equal to the original object.} {/eq}

    • {eq}\text{The final image is upright, virtual, and 3 times larger than the original object.} {/eq}

    • {eq}\text{The final image is 2 times smaller than the original object.} {/eq}

  • 2.

    We have two similar lenses, both of them are separated by a distance of 23 cm from each other. If an object is situated at 15 cm from lens 1, find out the height of the image formed by lens 2 (final image), if the length of the object is 8 cm.

    Answers:

    • {eq}1.9 \text{ cm } {/eq}

    • {eq}6.9 \text{ cm } {/eq}

    • {eq}4.6 \text{ cm } {/eq}

    • {eq}16 \text{ cm } {/eq}

  • 3.

    We have two similar lenses, both of them are separated by a distance of 23 cm from each other. If an object is situated at 15 cm from lens 1, predict the nature of the final image formed by lens 2, if the length of the object is 8 cm.

    Answers:

    • {eq}\text{The final image will be upright, real, and almost 4 times smaller than the object.} {/eq}

    • {eq}\text{The final image will be inverted, virtual, and almost 2 times smaller than the object.} {/eq}

    • {eq}\text{The final image will be upright, real, and almost 2 times smaller than the object.} {/eq}

    • {eq}\text{The final image will be upright, real, and almost 4 times larger than the object.} {/eq}

  • 4.

    There are two similar convex lenses situated at 27 cm from each other. An object of length 7 cm is situated at 10 cm from lens 1, what will be the height of the image formed by lens 2?

    Answers:

    • {eq}8.5 \text{cm} {/eq}

    • {eq}7.5 \text{cm} {/eq}

    • {eq}7 \text{cm} {/eq}

    • {eq}10.5 \text{cm} {/eq}

  • 5.

    There are two similar convex lenses situated at 24 cm from each other. An object of length 7 cm is situated at 10 cm from lens 1, which of the following is the correct option for the image formed by lens 2?

    Answers:

    • {eq}\text{The final image will be virtual, inverted, and 1.5 times smaller than the original object.} {/eq}

    • {eq}\text{The final image will be real, upright, and 1.5 times smaller than the original object.} {/eq}

    • {eq}\text{The final image will be virtual, upright, and 2.5 times larger than the original object.} {/eq}

    • {eq}\text{The final image will be real, upright, and 1.5 times larger than the original object.} {/eq}

  • 6.

    Look at the given diagram and find out the location and height of the final image formed by lens 2 if both the lenses are separated by a distance of 27 cm.

    Answers:

    • {eq}\text{The height of the final image will be 12 cm and it will be situated at 9 cm right of lens 1.} {/eq}

    • {eq}\text{The height of the final image will be 9 cm and it will be situated at 12 cm right of lens 1.} {/eq}

    • {eq}\text{The height of the final image will be 12 cm and it will be situated at 9 cm right of lens 2.} {/eq}

    • {eq}\text{The height of the final image will be 9 cm and it will be situated at 12 cm right of lens 2.} {/eq}

  • 7.

    Select the correct option regarding the location of the image formed by the lens 2 if the object and lenses are situated as shown in the given figure (the separation between both the lenses is 24 cm) :

    Answers:

    • {eq}\text{The image will be formed at 18 cm right side of the lens 2.} {/eq}

    • {eq}\text{The image will be formed at 18 cm left side of the lens 2.} {/eq}

    • {eq}\text{The image will be formed at 18 cm right side of the lens 1.} {/eq}

    • {eq}\text{The image will be formed at 18 cm left side of the lens 1.} {/eq}

  • 8.

    What will be the nature of the final image formed by the lens 2, if the object and lenses are as shown in the given figure?

    (The separation between both the lenses is 24 cm.)

    Answers:

    • {eq}\text{The final image will be real, upright, and 3 times smaller than the object.} {/eq}

    • {eq}\text{The final image will be real, inverted, and 3 times smaller than the object.} {/eq}

    • {eq}\text{The final image will be virtual, upright, and 3 times smaller than the object.} {/eq}

    • {eq}\text{The final image will be real, upright, and 3 times larger than the object.} {/eq}

  • 9.

    What will be the height and location of the final image if an object of the height of 8 cm is situated at 10.8 cm from lens 1 as shown in the given figure? (The separation between both lenses is 17 cm.)

    Answers:

    • {eq}\text{Height = 4.82 cm } \\ \text{Location = 14.29 cm left side from lens 1} {/eq}

    • {eq}\text{Height = 12.80 cm } \\ \text{Location = 14.30 cm right side from lens 2} {/eq}

    • {eq}\text{Height = 14.29 cm } \\ \text{Location = 12.82 cm left side from lens 1} {/eq}

    • {eq}\text{Height = 12.82 cm } \\ \text{Location = 14.29 cm left side from lens 1} {/eq}

  • 10.

    What will be the total magnification, if two lenses are situated as shown in the given figure? The separation between the lenses is 20 cm and the height of the object is 7 cm.

    Answers:

    • {eq}0.5 {/eq}

    • {eq}1.5 {/eq}

    • {eq}2.5 {/eq}

    • {eq}1 {/eq}

  • 11.

    Find the height of the final image formed by lens 2, if the lenses and the object are situated as given in the following figure. The separation between the lenses is 20 cm:

    Answers:

    • {eq}8.87 \text{ cm } {/eq}

    • {eq}14.13 \text{ cm } {/eq}

    • {eq}16.07 \text{ cm } {/eq}

    • {eq}7.15 \text{ cm } {/eq}

  • 12.

    What will be the final magnification if the object and lenses are as shown in the figure and the separation between the lenses is 20 cm? Write your answer up to 3 decimal places.

    Answers:

    • {eq}1.240 {/eq}

    • {eq}2.272 {/eq}

    • {eq}0.737 {/eq}

    • {eq}0.808 {/eq}

  • 13.

    What will be the position of the final image formed by lens 2 if the object is situated at 13.2 cm from lens 1 as shown in the given figure?

    Answers:

    • {eq}\text{9 cm right side of lens 2.} {/eq}

    • {eq}\text{14.5 cm right side of lens 2.} {/eq}

    • {eq}\text{6 cm right side of lens 2.} {/eq}

    • {eq}\text{13.2 cm right side of lens 2.} {/eq}

  • 14.

    The arrangement of lenses and the object is given in the following figure, what will be the nature of the final image formed by lens 2?

    Answers:

    • {eq}\text{Virtual and inverted.} {/eq}

    • {eq}\text{Real and inverted.} {/eq}

    • {eq}\text{Virtual and upright.} {/eq}

    • {eq}\text{Real and upright.} {/eq}

  • 15.

    What will be the height of the final image formed by lens 2, if the separation between the lenses is 19 cm? The height of the object is 8.25 cm. The object is situated at 12.77 cm left side of the lens 1.

    Answers:

    • {eq}26.24 \text{ cm } {/eq}

    • {eq}16.5 \text{ cm } {/eq}

    • {eq}4.13 \text{ cm } {/eq}

    • {eq}24.75 \text{ cm } {/eq}

  • 16.

    Locate the final image formed by lens 2 if the separation between both the lenses is 19 cm. The object is situated at 12.77 cm left side of the lens 1.

    Answers:

    • {eq}\text{7.69 cm left side of the lens 2. } {/eq}

    • {eq}\text{11.31 cm right side of the lens 1. } {/eq}

    • {eq}\text{12.77 cm right side of the lens 2. } {/eq}

    • {eq}\text{27.43 cm right side of the lens 2. } {/eq}

  • 17.

    Predict the nature of the final image formed by lens 2 if the arrangement of lenses and an object is shown in the given figure. Both the lenses are similar with a focal length of 7 cm.

    Answers:

    • {eq}\text{The final image will be real and inverted.} {/eq}

    • {eq}\text{The final image will be virtual and upright.} {/eq}

    • {eq}\text{The final image will be real and upright.} {/eq}

    • {eq}\text{The final image will be virtual and inverted.} {/eq}

  • 18.

    Suppose we have two similar lenses of focal length 5 cm situated as shown in the given figure. What will be the height, location, and nature of the final image formed by lens 2? (Height of the object is 12.85, Separation between the lenses is 23 cm. )

    Answers:

    • {eq}\text{Height = 38.55 cm } \\ \text{Location = 7.56 right side of the lens 1.} \\ \text{Nature = Virtual } {/eq}

    • {eq}\text{Height = 4.24 cm } \\ \text{Location = 7.56 right side of the lens 2.} \\ \text{Nature = Real } {/eq}

    • {eq}\text{Height = 6.38 cm } \\ \text{Location = 7.56 right side of the lens 2.} \\ \text{Nature = Virtual } {/eq}

    • {eq}\text{Height = 4.24 cm } \\ \text{Location = 7.56 left side of the lens 1.} \\ \text{Nature = Virtual } {/eq}

  • 19.

    Choose the correct option regarding the final image formed by lens 2. The location of an object and lenses is given in the following figure.

    Answers:

    • {eq}\text{The final image will be real and smaller than the original object.} {/eq}

    • {eq}\text{The final image will be real and larger than the original object.} {/eq}

    • {eq}\text{The final image will be virtual and larger than the original object.} {/eq}

    • {eq}\text{The final image will be virtual and smaller than the original object.} {/eq}

  • 20.

    What will be the distance of the final image from lens 2? The location of the object and lenses are given in the following figure.

    Answers:

    • {eq}\text{13.22 (left-side)} {/eq}

    • {eq}\text{13.22 (right-side)} {/eq}

    • {eq}\text{31.32 (right-side)} {/eq}

    • {eq}\text{31.32 (left-side)} {/eq}

  • 21.


    Using the above ray diagram, determine the nature of the final image produced by the combination of lenses, if an object is placed {eq}18\ \rm cm {/eq} in front of lens A and the focus of the lenses are {eq}12\ \rm cm {/eq}. Take the separation of the lenses as {eq}42\ \rm cm {/eq}.

    Answers:

    • The nature of the final image is upright, real, and {eq}4 {/eq} times as large as the original object.

    • The nature of the final image is upright, virtual, and {eq}4 {/eq} times as large as the original object.

    • The nature of the final image is inverted, virtual, and {eq}4 {/eq} times as large as the original object.

    • The nature of the final image is inverted, real, and {eq}4 {/eq} times as large as the original object.

  • 22.


    The above image shows that the two identical convex lenses ({eq}f=8\ \rm cm {/eq}) are separated by a distance of {eq}45\ \rm cm {/eq}. Choose the correct statement for the final image formed by the combination of the lenses.

    Answers:

    • The final image is a virtual image and is formed {eq}13.3\ \rm cm {/eq} to the right of lens 2.

    • The final image is a real image and is formed {eq}13.3\ \rm cm {/eq} to the right of lens 2.

    • The final image is a real image and is formed {eq}13.3\ \rm cm {/eq} to the left of lens 2.

    • The final image is a virtual image and is formed {eq}13.3\ \rm cm {/eq} to the left of lens 2.

  • 23.


    From the above ray diagram, determine the position of the final image from lens {eq}L_1 {/eq} if the separation between the lenses is equal to {eq}25\ \rm cm {/eq}.

    Answers:

    • {eq}12.73\ \rm cm {/eq} to the right of {eq}L_1 {/eq}.

    • {eq}25.73\ \rm cm {/eq} to the right of {eq}L_1 {/eq}.

    • {eq}37.73\ \rm cm {/eq} to the right of {eq}L_1 {/eq}.

    • {eq}24.73\ \rm cm {/eq} to the right of {eq}L_1 {/eq}.

  • 24.

    Calculate the total magnification of the final image produced by two identical converging lenses as shown in the diagram. The lenses are separated by a distance of {eq}60\ \rm cm {/eq}.


    Answers:

    • The total magnification of the final image will be equal to {eq}1.5 {/eq}.

    • The total magnification of the final image will be equal to {eq}1.1 {/eq}.

    • The total magnification of the final image will be equal to {eq}-1.1 {/eq}.

    • The total magnification of the final image will be equal to {eq}-1.5 {/eq}.

  • 25.


    Determine the type of final image produced by two identical convex lenses ({eq}f=30\ \rm cm {/eq}) as represented in the above ray diagram.

    Take the lens separation as {eq}12\ \rm cm {/eq}, and take that the object is placed at a distance of {eq}45\ \rm cm {/eq} in front of {eq}L_1 {/eq}

    Answers:

    • The final image produced is inverted, real and at a distance of {eq}21.67\ \rm cm {/eq} to the left of {eq}L_2 {/eq}.

    • The final image produced is inverted, real, and at a distance of {eq}21.67\ \rm cm {/eq} to the right of {eq}L_2 {/eq}.

    • The final image produced is inverted, virtual, and at a distance of {eq}21.67\ \rm cm {/eq} to the left of {eq}L_2 {/eq}.

    • The final image produced is upright, real, and at a distance of {eq}21.67\ \rm cm {/eq} to the right of {eq}L_2 {/eq}.

  • 26.


    Find the nature of the final image produced by the lenses as shown in the diagram. The lenses are separated by a distance of {eq}10\ \rm cm {/eq} and an object is placed {eq}24\ \rm cm {/eq} in front of the first lens.

    ({eq}f_1=f_2=12\ \rm cm {/eq})

    Answers:

    • The final image produced is inverted, real, and has a magnification of {eq}0.46 {/eq} and is located {eq}6.46\ \rm cm {/eq} to the right of lens {eq}L_2 {/eq}.

    • The final image produced is upright, virtual, and has a magnification of {eq}0.46 {/eq} and is located {eq}6.46\ \rm cm {/eq} to the right of lens {eq}L_2 {/eq}.

    • The final image produced is inverted, virtual, and has a magnification of {eq}0.46 {/eq} and is located {eq}6.46\ \rm cm {/eq} to the right of lens {eq}L_2 {/eq}.

    • The final image produced is upright, real, and has a magnification of {eq}0.46 {/eq} and is located {eq}6.46\ \rm cm {/eq} to the right of lens {eq}L_2 {/eq}.

  • 27.

    Which statement correctly represents the final image produced by the combination of lenses as shown in the diagram?


    Assume the object is placed at a distance of {eq}10\ \rm cm {/eq} in front of the first lens.

    Answers:

    • The final image is produced {eq}672\ \rm cm {/eq} to the right of {eq}L_2 {/eq}.

    • The final image is produced {eq}672\ \rm cm {/eq} to the left of {eq}L_1 {/eq}.

    • The final image is produced {eq}672\ \rm cm {/eq} to the right of {eq}L_1 {/eq}.

    • The final image is produced {eq}672\ \rm cm {/eq} to the left of {eq}L_2 {/eq}.

  • 28.

    Find the nature of the final image produced by two identical converging lenses as shown in the diagram. The lenses are separated by a distance of {eq}20\ \rm cm {/eq} and the focal length is equal to {eq}5\ \rm cm {/eq}.


    Answers:

    • The final image produced is virtual, upright, and magnified {eq}5 {/eq} times the size of the original object.

    • The final image produced is real, inverted, and magnified {eq}5 {/eq} times the size of the original object.

    • The final image produced is virtual, inverted, and magnified {eq}5 {/eq} times the size of the original object.

    • The final image produced is real, upright, and magnified {eq}5 {/eq} times the size of the original object.

  • 29.

    Two identical converging lenses of focal length {eq}30\ \rm cm {/eq} are separated by a distance of {eq}10\ \rm cm {/eq}. If an object is located at a distance of {eq}18\ \rm cm {/eq} as shown in the diagram, then the location of the final image produced will be equal to which of the following?


    Answers:

    • The position of final image will be {eq}45\ \rm cm {/eq} to the right of lens {eq}L_1 {/eq}.

    • The position of final image will be {eq}45\ \rm cm {/eq} to the right of lens {eq}L_2 {/eq}.

    • The position of final image will be {eq}66\ \rm cm {/eq} to the right of lens {eq}L_2 {/eq}.

    • The position of final image will be {eq}66\ \rm cm {/eq} to the right of lens {eq}L_1 {/eq}.

  • 30.


    Determine the position of the final image formed by lens B if the original object is located {eq}20\ \rm cm {/eq} to the left of lens A.

    Answers:

    • {eq}13\ \rm cm {/eq} to the right of lens B.

    • {eq}15\ \rm cm {/eq} to the right of lens B.

    • {eq}15\ \rm cm {/eq} to the left of lens B.

    • {eq}13\ \rm cm {/eq} to the left of lens B.

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