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?

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.

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Astronomical Telescope

Q: A astronomical telescope has objective and eyepiece of focal lengths \$40\ cm\$ and \$4\ cm\$ respectively. To view an object \$200\ cm\$ away from the objective, the lenses must be separated by a distance:

On applying the lens formula for the objective lens:\$\dfrac{1}{f_0}=\dfrac{1}{v_0}-\dfrac{1}{u_0}\$\$\dfrac{1}{v_0}=\dfrac{1}{f_0}+\dfrac{1}{u_0}\$\$\dfrac{1}{v_0}=\dfrac{1}{40}+\dfrac{1}{-200}\$\$v_0=50\ cm\$Therefore, tube length \$=v_0+f_e=50+4=54\ cm\$

Q: Draw a labeled ray diagram of a refracting telescope. Define its magnifying power and write the expression for it. Write two important limitation of a refracting telescope over a reflecting type telescope

Refracting telescope:Magnifying power- The magnifying power is the ratio of the angle \$\alpha\$ subtended at the eye by the final image to the angle \$\beta\$ which the object subtends at the lens or the eye.\$\displaystyle m=\frac{\beta}{\alpha}=\frac{h}{f_{e}}\frac{f_{0}}{h}=\frac{f_{0}}{f_{e}}\$Limitations of refracting telescope over reflecting type telescope-(i) Refracting telescope suffers from chromatic aberrations as it uses large sized lenses.(iii) The requirement of big lenses tend to be very heavy and therefore difficult to make and support by their edges

Q: Draw a labelled ray diagram of a reflecting telescope. Mention its two advantages over the refracting telescope.

Advantages of reflecting telescope over a refracting telescope-1. A large aperture is not required to focus incoming light, hence it is easy to manufacture.2. No spherical aberration exists, and thus a clear image is formed.

Q: Write two advantages of a reflecting telescope over a refracting telescope.

There is no chromatic aberration as the objective is a mirror in reflecting type telescope. Also the image is brighter compared to the one formed in refracting type telescope.

Q: The magnifying power of a telescope with tube length \$60cm\$ is \$5\$. What is the focal length of its eye piece?

The magnifying power of a telescope is given by\$m = \dfrac{f_0}{f_e}, \, 5 = \dfrac{f_0}{f_e}\$\$f_0 + f_e = 60\$ [The total length of the telescope is \$60cm\$]And \$f_0 = 5f_e\$\$\therefore f_0 + f_e = 5f_0, \, 6f_e = 60, f_e = 10cm\$\$f_0 = 5f_e = 50cm\$\$\therefore\$ The focal length of the eyepiece is \$f_e = 10cm\$

Q: A Cassegrain telescope uses two mirrors as shown in above figure. Such a telescope is built with the mirrors \$20\,mm\$ apart. If the radius of curvature of the large mirror is \$220\,mm\$ and the small mirror is \$140\,mm\$, where will the final image of an object at infinity be?

Distance between the objective mirror and the secondary mirror, \$d=20mm\$Radius of curvature of the objective mirror, \$R_1=220mm\$Hence, focal length of the objective mirror, \$f_1=R_1/2=110mm\$Radius of curvature of the secondary mirror, \$R_2=140mm\$Hence, focal length of the secondary mirror, \$f_2=R_2/2=70mm\$The image of an object placed at infinity, formed by the objective mirror, will act as a virtual object for the secondary mirror.Hence, the virtual object distance for the secondary mirror, \$u=f_1-d=110-20=90mm\$Applying the mirror formula for the secondary mirror,\$1/v+1/u=1/f_2\$\$\Rightarrow v=315mm\$Hence, the final image will be formed \$315 mm\$ away from the secondary mirror.

Q: Draw a schematic diagram of a reflecting telescope (Cassegrain). Write its two advantages over a refracting telescope.

Reflecting telescopes have many advantages over refracting telescopes.Mirrors don't cause chromatic aberration and they are easier and cheaper to build large. They are also easier to mount because the back of the mirror can be used to attach to the mount.

Q: Draw a schematic ray diagram reflecting telescope showing how rays coming from a distant object are received at eye piece. Write its two important advantages over a refracting telescope.

Advantages of reflecting telescope over a refracting telescope are:There is no chromatic aberration for reflecting telescope as the objective is a mirror.Spherical aberration is reduced in the case of reflecting telescopes by using mirror objective in the form of a paraboloid.

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