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Assertion If a lens is immersed in a liq...

Assertion If a lens is immersed in a liquid its nature will change ie., convex will behave concave and vice-versa.
Reason If both sides of a lens medium is same, then object can be placed on either side of the lens, image distance remains same

A

If both Assertion and Reason are true and Reason is the correct explanation of Assertion.

B

If both Assertion and Reason are true but Reason is not correct explanation of Assertion.

C

If Assertion is true but Reason is false.

D

If Assertion is false but Reason is true.

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 1: Understand the Assertion The assertion states that if a lens is immersed in a liquid, its nature will change, meaning a convex lens will behave like a concave lens and vice versa. ### Step 2: Analyze the Lens Maker's Formula The lens maker's formula is given by: \[ \frac{1}{f} = \frac{\mu_{\text{lens}}}{\mu_{\text{surrounding}} - 1} \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \] Where: - \( f \) is the focal length of the lens, - \( \mu_{\text{lens}} \) is the refractive index of the lens material, - \( \mu_{\text{surrounding}} \) is the refractive index of the surrounding medium, - \( R_1 \) and \( R_2 \) are the radii of curvature of the lens surfaces. ### Step 3: Calculate Focal Length in Air For a convex lens in air: - Assume \( \mu_{\text{lens}} = \frac{3}{2} \) (for glass), - \( \mu_{\text{surrounding}} = 1 \) (for air), - The focal length \( f_A \) will be positive. Using the lens maker's formula: \[ \frac{1}{f_A} = \frac{\frac{3}{2}}{1 - 1} \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \implies f_A > 0 \] This indicates that the lens converges light. ### Step 4: Calculate Focal Length in Water Now, if the lens is submerged in water: - Assume \( \mu_{\text{surrounding}} = \frac{4}{3} \) (for water), - The focal length \( f_W \) will be calculated as follows: \[ \frac{1}{f_W} = \frac{\frac{3}{2}}{\frac{4}{3} - 1} \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \] Simplifying gives: \[ \frac{1}{f_W} = \frac{\frac{3}{2}}{\frac{1}{3}} \left( \frac{1}{R_1} - \frac{1}{R_2} \right) = 4 \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \] Thus, \( f_W \) remains positive, indicating that the lens still converges light. ### Step 5: Conclusion on Assertion Since the focal length remains positive when the lens is submerged in water, the assertion that a convex lens behaves like a concave lens when immersed in a liquid is **false**. ### Step 6: Understand the Reason The reason states that if both sides of a lens medium are the same, the object can be placed on either side of the lens, and the image distance remains the same. ### Step 7: Analyze the Reason Using the lens formula: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] If the refractive indices on both sides are the same, the focal length remains the same regardless of which side the object is placed. Thus, the image distance will indeed remain the same. ### Step 8: Conclusion on Reason The reason is **true**. ### Final Answer - Assertion: False - Reason: True - Therefore, the correct answer is that the assertion is false and the reason is true.

To solve the question, we need to analyze both the assertion and the reason provided. ### Step 1: Understand the Assertion The assertion states that if a lens is immersed in a liquid, its nature will change, meaning a convex lens will behave like a concave lens and vice versa. ### Step 2: Analyze the Lens Maker's Formula The lens maker's formula is given by: \[ ...
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