Question

A basketball player of height 2.40 m is standing 2.60 m in front of a convex spherical mirror of radius of curvature 4.00 m. Determine the size of the image.

Answer 1

Answer:

The size of the image is 1.04 m.

Explanation:

Given that,

Height of object = 2.40 m

Distance of object = 2.60 m

Radius of curvature =4.00 m

Focal length $f=\dfrac{R}{2}=\dfrac{4.00}{2}=2.00$

We need to calculate the image distance

Using mirror formula

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

$\dfrac{1}{v}=\dfrac{1}{2.00}+\dfrac{1}{2.60}$

$\dfrac{1}{v}= \dfrac{23}{26}$

$v=1.13\ cm$

We need to calculate the height of the image

Using formula of magnification

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

Put the value into the formula

$\dfrac{h'}{2.40}=-\dfrac{1.13}{-2.60}$

$h'=\dfrac{1.13}{2.60}\times2.40$

$h'=1.04\ m$

Hence, The size of the image is 1.04 m