Question

Two thin convex lenses of focal length 10 cm and 15 cm are separated by a distance of 10 cm. The focal length of the combination is :-

• A. 4.2 cm
• B. 6 cm
• C. 10 cm
• D. 15 cm

Answer 1

Answer: (C)

10 cm

Answer 2

The equivalent focal length $F$ of a combination of two thin lenses with focal lengths $f_1$ and $f_2$ separated by a distance $d$ is given by the formula: $\frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2} - \frac{d}{f_1 f_2}$ Given: $f_1 = 10$ cm $f_2 = 15$ cm $d = 10$ cm

Substituting these values into the formula: $\frac{1}{F} = \frac{1}{10 \text{ cm}} + \frac{1}{15 \text{ cm}} - \frac{10 \text{ cm}}{(10 \text{ cm})(15 \text{ cm})}$ $\frac{1}{F} = \frac{1}{10} + \frac{1}{15} - \frac{10}{150}$ $\frac{1}{F} = \frac{1}{10} + \frac{1}{15} - \frac{1}{15}$ The terms $\frac{1}{15}$ and $-\frac{1}{15}$ cancel out: $\frac{1}{F} = \frac{1}{10} \text{ cm}^{-1}$ Therefore, the equivalent focal length $F$ is: $F = 10 \text{ cm}$