an object of size 7 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm at what distance from the mirror should a screen be placed so that a sharp focused image can be formed? find the size and the nature of the image.
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Answer:
Given,
Object distance, u = -27
focal length, f= -18
Size of object, h= 7
Let image distance or where image formed on a screen is v =?
We know that mirror formula is
1/f= 1/v+1/u
1/-18 = 1/v+1/-27
1/-18= 1/v -1/27
1/v = -1/18+1/27
1/v= -3+2/54
1/v = -1/54
v = -54cm
Therefore, the image distance or what distance from the mirror should a screen be placed is -54cm.
Now, the size of object h, =7cm
Let size of image, h'=?
by magnification of mirror
m= -v/u or m = h'/h
m= -(-54) /-27
m= -2
m= h'/h
-2 = h'/7
7×-2 =h'
-14 = h'
m= -2
- sign represent,the nature of image is real inverted and no. represent the size of image is double the size of object which -14 cm.
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