A compound lens is made up of two lenses L and L' having powers +12 D and -8 D respectively. both the lenses are placed in contact. a pencil of height 5 cm is placed 40 cm from L. what is the size and the nature of the image formed by the compound lens?
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power of L= +12D
power of L'= -8D
power of combination= L+L' = ( 12D ) + ( -8D ) = 4D
=> p= 1/f(in m)
=> 4= 1/F
=> f= 1/4
=> f= 0.25m or 25cm
Now,
1/v - 1/-u = 1/f
1/v - 1/-40 = 1/25
1/v = 1/25 - 1/40
1/v = 3/200
3v = 200
v = 66.6 cm
=> h2/h1 = v/u
=> h2/5=66.6/40
=> h2 = 66.3 * 5/40
= 66.3/8= 8.2cm
The nature of image is virtual and erect.
power of L'= -8D
power of combination= L+L' = ( 12D ) + ( -8D ) = 4D
=> p= 1/f(in m)
=> 4= 1/F
=> f= 1/4
=> f= 0.25m or 25cm
Now,
1/v - 1/-u = 1/f
1/v - 1/-40 = 1/25
1/v = 1/25 - 1/40
1/v = 3/200
3v = 200
v = 66.6 cm
=> h2/h1 = v/u
=> h2/5=66.6/40
=> h2 = 66.3 * 5/40
= 66.3/8= 8.2cm
The nature of image is virtual and erect.
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