question_answer

Two best friends John and Jolly are students of \[XI{{I}^{th}}\] class, John wants to be an astronaut but he does not know anything about astronomy. So, he shared his desire with his friend Jolly. Jolly asked him to take advice from his teacher.

(i) In which chapter John would be keen to learn astronomy and what should he do?

(ii) Draw ray diagram of terrestrial telescope.

(iii) Calculate the separation between two points on the moon that can be resolved using 550 cm telescope. The distance between the moon and the earth is \[3.8\times {{10}^{8}}m.\] The wavelength most sensitive to human eye is \[5500\,\overset{{}^\circ }{\mathop{A}}\,.\]

Answer:

(iii) 46.36 m (i) Ray optics chapter well and this purpose he should pursue astronomy for higher studies. (ii) (iii) Given, \[D=550\,cm=5.5\,m,\,\,\lambda =5500\,{\AA}\] \[=5.5\times {{10}^{-7}}m\] Since, limit of resolution, \[d\theta =\frac{1.22\lambda }{D}\] \[=\frac{1.22\times 55\times {{10}^{-7}}}{5.5}\] \[=1.22\times {{10}^{-7}}\text{rad}\] Here, \[\text{OA=OB=3}\text{.8}\times \text{1}{{\text{0}}^{8}}m\] Or         \[d=3.8\times {{10}^{8}}m\] \[\therefore \]      \[d\theta =\frac{x}{d}\] \[\Rightarrow \]   \[x=d\times d\theta =3.8\times {{10}^{8}}\times 1.22\times {{10}^{-7}}\] \[\therefore \]      \[x=46.36\,m\]