0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Question

The aperture diameter of a telescope is $$5m$$. The separation between the moon and the earth is $$4\times 10^5$$ km. With light of wavelength of $$5500\overset{o}{A}$$, the minimum separation between objects on the surface of moon, so that they are just resolved, is close to?

A
$$20$$ m
B
$$60$$ m
C
$$600$$ m
D
$$200$$ m
Solution
Verified by Toppr

Correct option is A. $$60$$ m
Refer above image.

Let the aperture $$=d$$ $$D=4\times 10^8m$$

$$wavelength =\lambda=5500\times 10^{-10}m$$

for two objects to be resolved

$$\theta=1.22\dfrac{\lambda}{d}$$

also $$d=D\theta$$

$$\Rightarrow \theta=\dfrac{d}{D}$$

$$\Rightarrow \dfrac{d}{4\times 10^8}=\dfrac{1.22\times 5500\times 10^{-10}}{5}$$

$$d=53.68\approx 60m$$

Option A is correct.


Was this answer helpful?
4
Similar Questions
Q1
The aperture diameter of a telescope is $$5m$$. The separation between the moon and the earth is $$4\times 10^5$$ km. With light of wavelength of $$5500\overset{o}{A}$$, the minimum separation between objects on the surface of moon, so that they are just resolved, is close to?
View Solution
Q2
The aperture of the largest telescope in the world is 5m, if the separation between the Moon and the Earth is 4×105km and the wavelength of the visible light is 5000oA then the minimum separation between the objects on the surface of the Moon which can be just resolve is approximately
View Solution
Q3

A telescope of aperture diameter 5m is used to observe the moon from the earth. Distance between the moon and earth is 4×105km. The minimum distance between two points on the moon’s surface which can be resolved using this telescope is close to (Wavelength of light is 5500A)


View Solution
Q4
The average distance between the earth and moon is $$38.6\times 10^4 km$$. The minimum separation between the two points on the surface of the moon that can be resolved by a telescope whose objective lens diameter of $$5\ m$$ with $$\lambda =6000\overset {o}{A}$$ is
View Solution
Q5
The distance of the moon from earth is $$3.8\times 10^5 km$$. The eye is most sensitive to light of wavelength $$5500\ \overset{o}{A}$$. The separation of two points on the moon that can be resolved by a $$500\ cm$$ telescope will be
View Solution