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Assertion A hollow lens behaves like a t...

Assertion A hollow lens behaves like a thin glass plate.
Reason Power of this lens becomes zero.

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 regarding the assertion and reason about a hollow lens, we can follow these steps: ### Step 1: Understand the Concept of a Hollow Lens A hollow lens is a lens that is empty inside, meaning it has no material in its center. It can be thought of as a lens with air or vacuum inside. The refractive index of the hollow lens will be the same as that of the surrounding medium (usually air). **Hint:** Consider the refractive index of the materials involved when analyzing the behavior of the lens. ### Step 2: Apply the Lensmaker's Formula The lensmaker's formula is given by: \[ \frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \] where \( f \) is the focal length, \( \mu \) is the refractive index of the lens material, and \( R_1 \) and \( R_2 \) are the radii of curvature of the lens surfaces. **Hint:** Remember that for a hollow lens, the refractive index (\( \mu \)) is equal to that of the surrounding medium. ### Step 3: Analyze the Focal Length of the Hollow Lens For a hollow lens, if the refractive index of the lens is the same as the surrounding medium (air), then: \[ \mu = 1 \] Substituting this into the lensmaker's formula, we get: \[ \frac{1}{f} = (1 - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) = 0 \] This implies that the focal length \( f \) is infinite. **Hint:** An infinite focal length indicates that the lens does not converge or diverge light rays. ### Step 4: Determine the Power of the Lens The power \( P \) of a lens is given by the formula: \[ P = \frac{1}{f} \] Since we found that \( f \) is infinite, the power becomes: \[ P = \frac{1}{\infty} = 0 \] **Hint:** Recall that power is a measure of how strongly a lens converges or diverges light. ### Step 5: Relate the Hollow Lens to a Thin Glass Plate A thin glass plate does not converge or diverge light; it simply transmits it. Since the hollow lens behaves similarly (with power zero), it can be said to act like a thin glass plate. **Hint:** Consider how light behaves when passing through different optical elements. ### Conclusion Both the assertion and reason are true. The hollow lens behaves like a thin glass plate, and its power is indeed zero. **Final Answer:** Both the assertion and reason are true, and the reason is the correct explanation of the assertion.

To solve the question regarding the assertion and reason about a hollow lens, we can follow these steps: ### Step 1: Understand the Concept of a Hollow Lens A hollow lens is a lens that is empty inside, meaning it has no material in its center. It can be thought of as a lens with air or vacuum inside. The refractive index of the hollow lens will be the same as that of the surrounding medium (usually air). **Hint:** Consider the refractive index of the materials involved when analyzing the behavior of the lens. ### Step 2: Apply the Lensmaker's Formula ...
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