Question

2. An object is placed in front of a convex mirror at a
distance numerically equal to the focal length of the
mirror. Find the image position. ​

Answer 1

Answer:

The image distance is half the distance of the object distance.

Explanation:

Let the distance of the object be x.

The focal length of the convex mirror = x

Now, image position =?

Using mirror formula

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

f is focal length

v is image distance

u is object distance

$\dfrac{1}{x}=\dfrac{1}{v}+\dfrac{1}{-x}$

$\dfrac{1}{x}=\dfrac{1}{v}-\dfrac{1}{x}$

$\dfrac{1}{v}=\dfrac{1}{x}+\dfrac{1}{x}$

$\dfrac{1}{v}=\dfrac{2}{x}$

$v = \dfrac{x}{2}$

Hence, the image distance is half the distance of the object distance.