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

The size of the image is 1.04 m.

Step-by-step explanation:

Given that,

Height of object = 2.40 m

Distance of object = 2.60 m

Radius of curvature =4.00 m

Focal length
`f=(R)/(2)=(4.00)/(2)=2.00`

We need to calculate the image distance

Using mirror formula

`(1)/(f)=(1)/(v)+(1)/(u)`

`(1)/(v)=(1)/(2.00)+(1)/(2.60)`

`(1)/(v)= (23)/(26)`

`v=1.13\ cm`

We need to calculate the height of the image

Using formula of magnification

`m=(h')/(h)=-(v)/(u)`

Put the value into the formula

`(h')/(2.40)=-(1.13)/(-2.60)`

`h'=(1.13)/(2.60)*2.40`

`h'=1.04\ m`

Hence, The size of the image is 1.04 m