Question

Diameter of the objective lens of a telescope is 250cm. For light of wavelength 600nm coming from a distant object, the limit of resolution of the telescope is close to?

A.)$1.5\times {10}^{-7}rad$
B.)$2.0\times {10}^{-7}rad$
C.)$3.0\times {10}^{-7}rad$
D.)$4.5\times {10}^{-7}rad$

Answer 1

Hint- This question can be directly approached by the formula of the limit of resolution or the resolving power for telescope i.e. ${\displaystyle \frac{1.22\lambda }{d}}$ , where $\lambda$ is the wavelength of the light coming from the distant source and d is the diameter of the objective of the lens of the telescope.


Complete answer:
Since the limit of resolution for telescope = ${\displaystyle \frac{1.22\lambda }{d}}$

Given the diameter of aperture of telescope, i.e. $d$=250cm

And the wavelength of the light coming from distant object, $\lambda$ = 600nm

Equalizing the units of $\lambda$ and $d$ to S.I. units:

$\lambda$ = 600nm = 600\times {10^{ - 9}}$m$d$=250cm=250\times {10}^{-2}$ m

Substituting these values in the direct formula of limit of resolution for the telescope, we get
$\Rightarrow$ Limit of resolution = ${\displaystyle \frac{1.22\lambda }{d}}$

$\Rightarrow$ Limit of resolution $={\displaystyle \frac{1.22(600)({10}^{-9})}{250({10}^{-2})}}$
$\Rightarrow$ Limit of resolution = 2.95 x 10^-7 rad

Taking its approximate value, we get

Limit of resolution for the given telescope 3.0 x 10^-7rad

Therefore, option (C) is the correct answer.

Note- The formula for limit of resolution should be known for the particular optical instrument as per the question. $\lambda$ and $d$ should not be confused with each other and the units must be kept the same , preferably according to the S.I. units. Any discrepancy regarding the units may lead to incorrect answers. It should be noted that the formula for different optical instruments is not the same. Also the limit of resolution and resolving power is the same.