Question

An astronomer is trying to observe two distant stars. The stars are marginally resolved when she looks at them through a filter that passes green light with a wavelength near 550 nm. Which of the following actions would improve the resolution? Assume that the resolution is not limited by the atmosphere.

A. Changing the filter to a different wavelength. If so, should she use a shorter or a longer wavelength?

B. Using a telescope with an objective lens of the same diameter but a different focal length. If so, should she select a shorter or a longer focal length?

C. Using a telescope with an objective lens of the same focal length but a different diameter. If so, should she select a larger or a smaller diameter?

D. Using an eyepiece with a different magnification. If so, should she select an eyepiece with more or less magnification?

Short answer

Part A) Improved

Part B) No change

Part C) Improved

Part D) No change

Step-by-step solution

Part A) .Step 1: Given Information

Wavelength $\lambda =550nm$

Par A). Step 2: Simplify

We know that angular resolution of telescope is given by,

${\theta }_{min}=\frac{1.22\lambda }{D}$

Two objects are said to be marginally resolvable if localid="1649406994660" $\alpha ={\theta }_{min}$and are said to be resolvable if $\alpha >{\theta }_{min}$

Therefore, Decreasing wavelength decreases ${\theta }_{min}$which makes role="math" localid="1649406982932" $\alpha >{\theta }_{min}$so the resolution is improved.

Part B)  Step 1: Given information 

The lens has same diameter but a different focal length.

Part B) Step 2.simplify

We know that angular resolution of telescope is given by,

${\theta }_{min}=\frac{1.22\lambda }{D}$

Therefore, f is not in the formula for resolution, hence this will not do anything.

Part C) step 1: Given Information

objective lens have same focal length but a different diameter.

Part C) Step 2.simplify

Angular resolution of telescope is,

${\theta }_{min}=\frac{1.22\lambda }{D}$

Two objects are said to be marginally resolvable if $\alpha ={\theta }_{min}$and are said to be resolvable if localid="1649406939654" $\alpha >{\theta }_{min}$

Increasing D (as lens size is increased) decreases ${\theta }_{min}$which makes $\alpha >{\theta }_{min}$ .

Part D) Step 1. Given information

eyepiece of different magnification.

Part D) Step 2.Simplify

Angular resolution of telescope is,

${\theta }_{min}=\frac{1.22\lambda }{D}$

Magnification plays no role in the above formula.