Question

A bright object 50 mm high stands on the axis of a concave mirror of focal length 100 mm and at a distance of 300 mm from the concave mirror. How big will the image be?

Answer 1

Distance of the object from the mirror 'u' = -300 mm

Height of the object 'h_o' = 50 mm

Focal length of the mirror 'f' = -100 mm

We have to find the distance of the image 'v' and the height of the image 'h_i'. 

`1/f=1/v+1/u` 

`1/-100=1/v+1/-300` 

`-1/100=1/v-1/300` 

`1/v=1/300-1/100` 

`1/v=1/300-1/100` 

`1/v=(-2)/300` 

v=-150 cm  

Thus, the image will be at a distance of 150 mm in front of the mirror.Now, using the magnification formula, we

 get

`m=h_i/h_o=-v/u` 

`h_i/50=-(-150)/-300 =-1/2` 

`h_i=-50/2=-25 mm` 

Thus, the size of the image will be 25 mm.