Question

Two thin lenses are in contact and the focal length of the combination is $80cm$. If the focal length of one lens is $20cm$, then the power of the other lens will be

• A. $-1.00D$
• B. $1.66D$
• C. $-3.75D$
• D. $4.00D$

Answer 1

The correct option is C

$-3.75D$

Step 1: Given data

Given the focal length of a combination of lenses $f=80cm$

The focal length of one of the lenses is $f_2=20$ cm

Step 2: Evaluate the combined focal length of lenses-
We know that Combined focal length $\frac{1}{f_1}+\frac{1}{f_2}=\frac{1}{f}$

Therefore, $\frac{1}{f_1}=\frac{1}{f}-\frac{1}{f_2}=\frac{1}{80}-\frac{1}{20}=\frac{-80+20}{-80\times 20}=\frac{-60}{1600}=-\frac{3}{80}c{m}^{-1}$

Thus, $\frac{1}{f_1}=-\frac{3}{80}c{m}^{-1}$

Step 3: Convert into $m^{-1}$and calculate power-

Power of lens $P=\frac{1}{f}$

Therefore, the power of the lens $=-\frac{3}{80}c{m}^{-1}=-\frac{300}{80}{m}^{-1}=-3.75m^{-1}$

which can be written as $-3.75D$

Hence, the correct option is (c) $-3.75D$