A doublet is a combination of two lenses. One such doublet is made with a convex lens of focal length of 20 cm and a concave lens of focal length of 50 cm. The effective focal length and power of this doublet is _______ and _______, respectively.

Correct Option: (b) 33.3 cm, 3D

​Focal length of the convex lens $$(f_1) = +20 cm$$​

Focal length of the concave lens $$(f_2) = −50 cm$$​​

 Effective Focal Length

The formula for the effective focal length ($F$) of two lenses in combination is:

​$$\frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2}$$​​

​$$\frac{1}{F} = \frac{1}{20} + \frac{1}{-50}=\frac{5 - 2}{100} = \frac{3}{100}=33.33 cm$$​​

 Power of the Doublet

​$$P = \frac{100}{F (\text{in cm})}$$​​

Substitute $F=33.33\text{cm}$:

​$$P = \frac{100}{33.33} = 3 \, \text{D}$$​​

Effective focal length: 33.33 cm

Power: 3D

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