AIIMS 2005 Physics Telescopes Assertion Reason Question

To analyze the question regarding the resolving power of a telescope and the relationship between the diameter of the objective lens and light collection, let's break down both the assertion and the reason.

Assertion

The assertion states: "The resolving power of a telescope is more if the diameter of the objective lens is more."

Explanation: The resolving power of a telescope, which is the ability to distinguish between two closely spaced objects, is directly related to the diameter of the objective lens (or mirror). The formula that captures this relationship is given by:

$$\text{Resolving Power} = \frac{1.22 \lambda}{D}$$

where:

• $\lambda$ is the wavelength of light used,
• $D$ is the diameter of the objective lens.

From this formula, it is clear that as the diameter $D$ increases, the resolving power (ability to resolve details) also increases because the denominator becomes larger, which results in a smaller value for the resolving power. Thus, the assertion is true.

Reason

The reason states: "Objective lens of large diameter collects more light."

Explanation: A larger diameter lens indeed collects more light due to its increased surface area. The area $A$ of a circular lens can be calculated using the formula:

$$A = \pi \left( \frac{D}{2} \right)^2 = \frac{\pi D^2}{4}$$

As the diameter $D$ increases, the area increases proportionally to the square of the diameter, which allows the telescope to gather more light. This is important for observing faint objects and contributes to better image quality.

Conclusion

Since both the assertion and the reason are true, and the reason effectively explains why a larger diameter improves resolving power (due to more light collection leading to better clarity and detail in images), the correct answer is:

A) Both assertion and reason are true and reason is the correct explanation of assertion.

Incorrect Options:

• B) Both assertion and reason are true but reason is not the correct explanation of assertion.

  • This option is incorrect because the reason does indeed explain why a larger diameter increases resolving power.

• C) Assertion is true but reason is false.

  • This option is incorrect since both the assertion and reason are true.

• D) Both assertion and reason are false.

  • This option is also incorrect as we have established both the assertion and reason as true.

In summary, the correct choice is A, supported by the understanding of how the diameter of the objective lens affects both the resolving power and light collection capabilities of the telescope.