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Assertion : The resolving power of a tel...

Assertion : The resolving power of a telescope is more if the diameter of the objective lens is more.
Reason : Objective lens of large diameter collectd more light.

A

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

B

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

C

c.If assertion is true but reason is false

D

d.If both assertion and reason are false

Text Solution

AI Generated Solution

The correct Answer is:
To solve the assertion and reason question, we will analyze both the assertion and the reason provided. ### Step-by-Step Solution: 1. **Understanding the Assertion**: - The assertion states that "The resolving power of a telescope is more if the diameter of the objective lens is more." - Resolving power (RP) is defined as the ability of a telescope to distinguish between two closely spaced objects. It is given by the formula: \[ RP = \frac{D}{1.22 \lambda} \] where \(D\) is the diameter of the objective lens and \(\lambda\) is the wavelength of light used. 2. **Analyzing the Assertion**: - From the formula, we see that resolving power (RP) is directly proportional to the diameter \(D\) of the objective lens. This means that as the diameter increases, the resolving power also increases. - Therefore, the assertion is **true**. 3. **Understanding the Reason**: - The reason states that "Objective lens of large diameter collects more light." - The light-gathering power of a telescope is indeed proportional to the area of the objective lens, which is related to the square of its diameter: \[ \text{Light Gathering Power} \propto D^2 \] - Hence, a larger diameter lens collects more light, making this statement also **true**. 4. **Evaluating the Relationship Between Assertion and Reason**: - While both the assertion and the reason are true, the reason does not correctly explain the assertion. The assertion is about resolving power, while the reason discusses light-gathering capability. - Therefore, we conclude that the assertion is true, the reason is true, but the reason is not the correct explanation for the assertion. ### Final Conclusion: - Assertion: True - Reason: True - Explanation: The reason does not explain the assertion.
To solve the assertion and reason question, we will analyze both the assertion and the reason provided. ### Step-by-Step Solution: 1. **Understanding the Assertion**: - The assertion states that "The resolving power of a telescope is more if the diameter of the objective lens is more." - Resolving power (RP) is defined as the ability of a telescope to distinguish between two closely spaced objects. It is given by the formula: \[ ...
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