What minimum separation between two objects a | vedclass

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

Question

(A) Given: Diameter of pupil, $d = 2 \,mm = 2 	imes 10^{-3} \,m$. Distance of objects, $D = 20 \,m$. Wavelength of light, $\lambda = 600 \,nm = 6 	i

Vedclass · Accepted Answer

$7.32$

Vedclass · Answer

(A) Given: Diameter of pupil, $d = 2 \,mm = 2 	imes 10^{-3} \,m$. Distance of objects, $D = 20 \,m$. Wavelength of light, $\lambda = 600 \,nm = 6 	imes 10^{-7} \,m$.The limit of resolution for a circular aperture (like the pupil of an eye) is given by the Rayleigh criterion:$	heta = \frac{1.22 \lambda}{d}$The minimum separation $y$ between two objects at distance $D$ is given by $y = 	heta 	imes D$.Substituting the values:$y = \frac{1.22 	imes 6 	imes 10^{-7} 	imes 20}{2 	imes 10^{-3}}$$y = 1.22 	imes 6 	imes 10^{-4} 	imes 10 = 7.32 	imes 10^{-3} \,m$$y = 7.32 \,mm$.Thus, the minimum separation the human eye can resolve is $7.32 \,mm$.

What minimum separation between two objects a human eye would be able to resolve, if the eye pupil diameter is $2 \,mm$ and the two objects are $20 \,m$ away from the eye (in $\,mm$)?
(Assume, human eye to be equivalent to a convex lens and consider the average wavelength of light as $600 \,nm$.)

Similar Questions

Explain the resolving power of optical instruments and explain the resolving power of telescopes.

If an object kept at the least distance of distinct vision is just resolved with light of wavelength $500 \ nm$ and a pupil of diameter $1 \ mm$,at what distance will the object be just resolved if the wavelength is $400 \ nm$ and the pupil diameter is $0.8 \ mm$ (in $cm$)?

The diameter of the objective lens of a telescope is $250\, cm$. For light of wavelength $600\, nm$ coming from a distant object, the limit of resolution of the telescope is close to:

The diameter of the objective lens of a microscope makes an angle $\beta$ at the focus of the microscope. Further,the medium between the object and the lens is an oil of refractive index $n$. Then the resolving power of the microscope

Wavelengths of light used in an optical instrument are $\lambda_1 = 4000 \; \mathring{A}$ and $\lambda_2 = 5000 \; \mathring{A}$. The ratio of their respective resolving powers (corresponding to $\lambda_1$ and $\lambda_2$) is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module

What minimum separation between two objects a human eye would be able to resolve, if the eye pupil diameter is $2 \,mm$ and the two objects are $20 \,m$ away from the eye (in $\,mm$)?(Assume, human eye to be equivalent to a convex lens and consider the average wavelength of light as $600 \,nm$.)