Question

A 17.0 cm tall cup is placed 75.5 cm away from the center of a concave mirror with a focal length of 39.0 cm. What is the height of the cup's mirror image?

Answer 1

Explanation:

It is given that,

Height of the object, h = 17 cm

Object distance, u = -75.5 cm

Focal length of the concave mirror, f = -39 cm

We need to find the height if the cup's mirror image. Let v is the image distance. Using mirror's equation as :

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

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

$\dfrac{1}{(-39)}-\dfrac{1}{(-75.5)}=\dfrac{1}{v}$

v = −80.67 cm

Let h' is the magnification of the mirror. The magnification of mirror is given by:

$m=\dfrac{-v}{u}=\dfrac{h'}{h}$

$h'=\dfrac{-vh}{u}$

$h'=\dfrac{-(-80.67)(17)}{-75.5}$

h' = −18.16 cm

So, the image of cup is 18.16 cm tall and it is inverted. Hence, this is the required solution.