An object of size 5 cm is placed at a distance of 20cm in front of concave mirror of radius of curvature 30cm.

a) Find the position of the image, its nature and size. 

b) Draw the corresponding ray diagram. 

Asked by sayantansaha225 | 26th May, 2021, 05:13: PM

Expert Answer:

 
We have mirror equation that is given by 
 
begin mathsize 14px style 1 over v space plus space 1 over u space equals space 1 over f end style
 
where v is mirror-to-image distance , u is mirror-to-object distance and f is focal length of mirror.
 
Object is placed at 20 cm in front of mirror , hence u = 20 cm
 
Radius of curvature of mirror R = 30 cm , hence focal length f = R/2 = 15 cm
 
Hence , we get ,  ( 1/ v ) = ( 1/15 ) - (1/20) =  ( 1 / 60 ) 
 
Hence we get , v = 60 cm
 
Image is formed at 60 cm in front of mirror.
 
Magnification m = - v/u = - 60/20 = - 3
 
Since size of object is 5 cm , size of image = -3 begin mathsize 14px style cross times end style 5 = -15 cm
 
Image is real, inverted and magnified.

Answered by Thiyagarajan K | 26th May, 2021, 10:43: PM