An object 1m tall is placed on the principal axis of a convex lens and its 40 cm tall image is formed on the screen at a distance of 70 cm from the object. Calculate the focal length of the lens.

Asked by Palak Shrivastava | 29th Nov, 2013, 07:43: PM

Expert Answer:

Since the image is formed on the screen, image is real and inverted.
 
Given that,
 
h = 1 m = 100 cm
h' = -40 cm
 
u + v = 70 cm
 
Let u = -x      v = 70 - x
 
focal length F = ?
 
Magnification m = h'/h = v/u
 
m = -40/100 = (70 - x)/(-x)
 
40x = 7000 - 100x
 
x = 50 cm
 
u = -x = -50 cm
v = 70 - x = 70 -50 = 20 cm
 
Substituting the values of u and v in the lens formula,
 
1/v - 1/u = 1/f
 
1/20 - 1/(-50) = 1/f
 
1/20 + 1/50 = 1/f
 
70/1000 = 1/f
 
f = 100/7
 
f = 14.3 cm
 
Hence the focal length of the lens is 14.3 cm.

Answered by Komal Parmar | 30th Nov, 2013, 12:41: AM

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