Question:
When a particular wave length of light is used, the focal length of a convex mirror is found to be 10 cm. If the wavelength of the incident light is doubled keeping the area of the mirror constant, the focal length of the mirror will be:
When a particular wave length of light is used, the focal length of a convex mirror is found to be 10 cm. If the wavelength of the incident light is doubled keeping the area of the mirror constant, the focal length of the mirror will be:
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The focal length of a convex mirror is directly proportional to the wavelength of the incident light, so doubling the wavelength will double the focal length, provided the area of the mirror remains constant.
Updated On: Apr 17, 2025
- 5 cm
- 20 cm
- 15 cm
- 10 cm
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The Correct Option is D
Solution and Explanation
In the case of a convex mirror, the focal length depends on the wavelength of the incident light and the mirror's area. The formula for the focal length \( f \) of a convex mirror in terms of the wavelength \( \lambda \) is given by:
\[
f \propto \lambda.
\]
This means that the focal length is directly proportional to the wavelength of the incident light, keeping the area of the mirror constant.
Given that the initial wavelength corresponds to a focal length of 10 cm, when the wavelength is doubled, the focal length will also double.
Thus, if the wavelength is doubled, the new focal length will be:
\[
f' = 2 \times f = 2 \times 10 \, \text{cm} = 10 \, \text{cm}.
\]
Therefore, the focal length of the mirror remains the same, i.e., \( 10 \, \text{cm} \), which corresponds to option (D).
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