Question

A combination of two thin lenses in contact have power $+10$D. The power reduces to $+6$D when the lenses are $0.25$ m apart. The power of individual lenses is

• A. 5D, 5D
• B. 6D, 4D
• C. 7D, 3D
• D. 8D, 2D

Hint:

Physics Tip: Lens powers add in contact, but subtract term $dP_1P_2$ when separated.

Answer 1

The Correct Option is D

Step 1: Power when lenses are in contact. For two thin lenses in contact: $$ P=P_1+P_2 $$ Given: $$ P_1+P_2=10 $$

Step 2: Power when separated by distance $d$. Equivalent power of two lenses separated by distance $d$ is: $$ P=P_1+P_2-dP_1P_2 $$ Given:
• $P=6$
• $d=0.25$ m So, $$ 6=P_1+P_2-0.25P_1P_2 $$

Step 3: Use $P_1+P_2=10$. $$ 6=10-0.25P_1P_2 $$ $$ 0.25P_1P_2=4 $$ $$ P_1P_2=16 $$

Step 4: Solve equations. Now we have: $$ P_1+P_2=10,\quad P_1P_2=16 $$ So quadratic equation: $$ x^2-10x+16=0 $$ $$ (x-8)(x-2)=0 $$ Thus: $$ P_1=8,\quad P_2=2 $$

Step 5: Conclusion. Hence individual lens powers are 8D and 2D. $$ \therefore \text{Correct option is (D).} $$