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Assertion : If a convex lens of glass is...

Assertion : If a convex lens of glass is immersed in water its power decreases.
Reason : In water it behaves as a convex lens.

A

If both the assertion and reason are true statement and reason is correct explanation of the assertion .

B

If both the assertion and reason are true statement but reason is not a correct explanation of the assertion .

C

If the assertion is true but the reason is a false statement.

D

If both assertion and reason are false statements.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze both the assertion and the reason provided. ### Step-by-Step Solution: 1. **Understanding the Assertion**: - The assertion states that "If a convex lens of glass is immersed in water, its power decreases." - The power (P) of a lens is given by the formula: \[ P = \frac{1}{f} \] where \( f \) is the focal length of the lens. The focal length of a lens depends on the refractive index of the lens material and the medium in which it is placed. 2. **Refractive Index Consideration**: - The refractive index of glass (n_glass) is typically greater than that of water (n_water). - When the lens is in air, the refractive index of the lens is compared to that of air (n_air). However, when the lens is immersed in water, the effective refractive index changes. 3. **Calculating Effective Focal Length**: - The formula for the focal length of a lens in a medium is given by: \[ \frac{1}{f} = (n_{lens} - n_{medium}) \cdot \frac{1}{R} \] where \( R \) is the radius of curvature of the lens. - When the lens is in water, the effective refractive index becomes \( n_{glass} - n_{water} \), which is less than \( n_{glass} - n_{air} \). - As a result, the focal length \( f \) increases, leading to a decrease in power \( P \). 4. **Understanding the Reason**: - The reason states that "In water it behaves as a convex lens." - This is true; a convex lens remains a convex lens regardless of the medium it is in. However, the power of the lens is affected by the refractive indices of the lens and the surrounding medium. 5. **Conclusion**: - The assertion is correct because the power of the lens decreases when immersed in water. - The reason is also correct, but it does not explain why the power decreases. It simply states that the lens behaves as a convex lens, which is true but does not address the change in power. ### Final Answer: - Both the assertion and reason are correct, but the reason is not the correct explanation for the assertion.

To solve the question, we need to analyze both the assertion and the reason provided. ### Step-by-Step Solution: 1. **Understanding the Assertion**: - The assertion states that "If a convex lens of glass is immersed in water, its power decreases." - The power (P) of a lens is given by the formula: \[ P = \frac{1}{f} \] ...
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