Question

An achromatic convergent doublet of two lenses in contact has a power of \(+2D\). The convex lens has power \(+5D\). What is the ratio of the dispersive powers of the convergent and divergent lenses?

• A. \(2:5\)
• B. \(3:5\)
• C. \(5:2\)
• D. \(5:3\)

Hint:

For an achromatic combination in contact, the sum of power times dispersive power of the lenses is zero.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
For two thin lenses in contact to be achromatic, the condition is
\(\dfrac{\omega_1}{f_1}+\dfrac{\omega_2}{f_2}=0\), that is \(\omega_1P_1+\omega_2P_2=0\).

Step 2: Find the Power of the Second Lens
Total power \(P=P_1+P_2=2\ \text{D}\) and \(P_1=+5\ \text{D}\).
\(P_2=2-5=-3\ \text{D}\)

Step 3: Calculation
\(\dfrac{\omega_1}{\omega_2}=-\dfrac{P_2}{P_1}=-\dfrac{-3}{5}=\dfrac{3}{5}\)

Step 4: Compare the options
The ratio of dispersive powers of convergent to divergent lens is \(3:5\), option (B).

Final Answer:
The dispersive powers of the convergent and divergent lenses are in the ratio 3 to 5. \[ \boxed{\text{(B) }3:5} \]