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Question

Physics Question on Ray optics and optical instruments

In the figure shown here, what is the equivalent focal length of the combination of lenses (Assume that all layers are thin)?
focal length of the combination of lenses

A

-40 cm

B

-100 cm

C

-50 cm

D

40 cm

Answer

-100 cm

Explanation

Solution

The correct option is (B): -100 cm

Use 1f=[μ−1][1R1−1R2]\frac{1}{f}=[\mu-1][\frac{1}{R_1}-\frac{1}{R_2}]

1f1=[1.6−1][1∞−120]=−3100\frac{1}{f_1}=[1.6-1][\frac{1}{\infty}-\frac{1}{20}]=\frac{-3}{100}

1f2[1.5−1][120+120]=120\frac{1}{f_2}[1.5-1][\frac{1}{20}+\frac{1}{20}]=\frac{1}{20}

1f3=−3100\frac{1}{f_3}=\frac{-3}{100}

1feq=1f1+1f2+1f3=−3100+120+−3100=−1100\frac{1}{f_{eq}}=\frac{1}{f_1}+\frac{1}{f_2}+\frac{1}{f_3}=\frac{-3}{100}+\frac{1}{20}+\frac{-3}{100}=\frac{-1}{100}
So, the correct option is (B) : -100 cm.