Question

An image by a concave mirror is 4 times greater than the object. If the radius of curvature is 20 cm:
A. Sketch the ray diagram of the above
B. Determine the object distance in front of the mirror.

Answer 1

Given:

An image by a concave mirror is 4 times greater than the object. The radius of curvature is 20 cm.

To find:

• Object distance from mirror
• Ray diagram

Calculation:

Let object distance be u and image distance be v;

$magnification = - \dfrac{v}{u}$

$= > 4 = - \dfrac{v}{u}$

$= > v = - 4u$

Applying Mirror Formula:

$\therefore \: \dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u}$

$= > \: \dfrac{1}{( - 10)} = \dfrac{1}{ ( - 4u)} + \dfrac{1}{u}$

$= > \: \dfrac{1}{( - 10)} = - \dfrac{1}{ 4u} + \dfrac{1}{u}$

$= > \: \dfrac{1}{( - 10)} = \dfrac{ - 1 + 4}{ 4u}$

$= > \: \dfrac{1}{( - 10)} = \dfrac{ 3}{ 4u}$

$= > \: \dfrac{1}{( - 2.5)} = \dfrac{ 3}{ u}$

$= > \: u = - 7.5\: cm$

So, final answer is:

$\boxed{ \sf{\: u = - 7.5 \: cm}}$

Answer 2

Explanation:

Answer is in the above figure

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