An object of size 7.0 cm is placed at 27 cm infront of a concave mirror of focal length 18 cm. At what distance from a mirror should a screen be placed, so that a sharp focused image can be obtained?Find the size and the nature of the image.

Asked by anangi.prathima | 12th Apr, 2020, 02:43: PM

Expert Answer:

ho = 7 cm
u = - 27 cm ( object is placed to left of mirror)
f =  - 18 cm (focal length of concave mirror)
By mirror formula,
1/f = 1/u + 1/v
1/ (-18) = 1/ (-27) + 1/ v 
1/ v = 1/ (-18) - 1/(-27)
Solving we get,
1/v = (-9)/486
1/v = - (1/54)
 v = -54 cm 
Thus,
The sharp image will be formed at 54 cm from concave mirror. 
Hence, screen must be placed at 54 cm from mirror.
By linear magnification,
-v/u = hi /ho 
- (-54)/(-27) = (hi)/ (7)
hi = - 14 cm 
Height of image is more than height of object
Thus, image formed is magnified.
m = -v/u = -(-54)/(-27) = - 2 
Image is twice the size of object.
Negative sign indicates that image formed is real, inverted and enlarged/magnified. 
 
 

Answered by Shiwani Sawant | 12th Apr, 2020, 03:48: PM