The aperture diameter of a telescope is 5; m. | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The angular resolution of a telescope is given by the formula $\Delta 	heta = \frac{1.22 \lambda}{D}$, where $\lambda$ is the wavelength of light

Vedclass · Accepted Answer

$60$

Vedclass · Answer

(C) The angular resolution of a telescope is given by the formula $\Delta 	heta = \frac{1.22 \lambda}{D}$, where $\lambda$ is the wavelength of light and $D$ is the diameter of the aperture.Given: $\lambda = 5500 \; \mathring{A} = 5500 	imes 10^{-10} \; m$, $D = 5 \; m$, and distance $d = 4 	imes 10^{5} \; km = 4 	imes 10^{8} \; m$.The linear separation $x$ between two objects on the moon that can be just resolved is given by $x = d \cdot \Delta 	heta$.Substituting the values:$x = d 	imes \frac{1.22 \lambda}{D} = \frac{4 	imes 10^{8} 	imes 1.22 	imes 5500 	imes 10^{-10}}{5}$.$x = \frac{4 	imes 1.22 	imes 5.5 	imes 10^{-2}}{5} 	imes 10^{8} = 0.8 	imes 1.22 	imes 5.5 	imes 10^{-2} 	imes 10^{8} = 53.68 \; m$.Rounding this value to the nearest provided option, we get $60 \; m$.

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

Similar Questions

When the wavelengths of light used in optical instruments $A$ and $B$ are $4500 \, \text{Å}$ and $6000 \, \text{Å}$ respectively, the ratio of the resolving power of $A$ to $B$ will be:

$A$ person is observing a bacteria through a compound microscope. For better analysis and to improve the resolving power,he should:

The human eye has an approximate angular resolution of $\phi = 5.8 \times 10^{-4} \, rad$ and a typical photoprinter prints a minimum of $300 \, dpi$ (dots per inch, $1 \, inch = 2.54 \, cm$). At what minimal distance $z$ should a printed page be held so that one does not see the individual dots?

If $f_{0} = 5 \, cm$,$\lambda = 6000 \, \mathring{A}$,and $a = 1 \, cm$ for a microscope,what will be its resolving power?

Vedclass Test Series

Exam Paper Generator

Online Exam Module