# A 5.0 cm real object is placed at a distance of 5.0 cm from a concave mirror of focal length 10...

## Question:

A 5.0 cm real object is placed at a distance of 5.0 cm from a concave mirror of focal length 10 cm. Find the size of the image.

A. 5 cm

B. 10 cm

C. 17 cm

D. 20 cm

A(n) _____ lens is used to produce a real image.

A. convex

B. concave

C. plane

D. diverging

## Lens Formula and Sign Conventions:

Lens formula is a relation between the focal length of the lens, the object and image distances from the lens. It is given by the equation;

{eq}\dfrac {1}{v}-\dfrac {1}{u} =\dfrac {1}{f}\\ {/eq}

where,

- {eq}v {/eq} is image distance,

- {eq}u {/eq} is object distance,

- {eq}f {/eq} is the focal length of the lens.

**Sign conventions:**

The image formation by the lens follows some sign conventions. These are;

- Distances is always measured from the optical center of the lens.
- Distances measured in the direction of the incident ray are taken as positive.
- Distances measured in the direction opposite to the incident ray are taken as negative.
- Distances measured above the principal axis are taken as positive.
- Distances measured below the principal axis are taken as negative.

## Answer and Explanation:

**Given**

- Distance of object from the mirror is {eq}u= -5\ cm {/eq}

- The focal length of the mirror is {eq}f= -10\ cm {/eq}

- The height of the object is {eq}h_o= 5\ cm {/eq}

**Let**

- {eq}v {/eq} is the distance of the image from the mirror.

- {eq}h_i {/eq} is the height of the image.

From the Mirror formula,

{eq}\begin{align} \dfrac {1}{f}&=\dfrac{1}{v}+\dfrac {1}{u}\\ \dfrac{1}{v}&= \dfrac{1}{f}-\dfrac{1}{u}\\ \dfrac{1}{v}&= \dfrac{1}{-10\ cm}-\dfrac{1}{-5\ cm}\\ implies v&=10\ cm\\ \end{align} {/eq}

The magnification of the image is given by

{eq}\begin{align} m &= -\dfrac {v}{u}\\ \dfrac{h_i }{h_o}&=-\dfrac {v}{u}\\ \dfrac{h_i}{5\ cm}&=-\dfrac{10\ cm}{-5\ cm}\\ \implies h_i &=10\ cm\\ \end{align} {/eq}

**Therefore, the height of the image formed is {eq}10\ cm {/eq} and hence option B. is right.**

In the second question, the option B. is correct. Because, only concave mirror produce a real image among the given options.

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from Physics 101: Help and Review

Chapter 14 / Lesson 17