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

Assertion $(A):$ To increase the resolving power of a telescope,the aperture $(a)$ of the objective lens should be large.
Reason $(R):$ The resolving power of a telescope is given by $\frac{a}{1.22 \lambda}$.

Which of the following is the smallest size grain that can be seen using a normal microscope using visible light $(400 \ nm < \lambda < 700 \ nm)$ (in $nm$)?

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

Two luminous point sources separated by a certain distance are at $10 \,km$ from an observer. If the aperture of his eye is $2.5 \times 10^{-3} \,m$ and the wavelength of light used is $500 \,nm$, the distance of separation between the point sources just seen to be resolved is (in $\,m$)

The headlights of a jeep are $1.2 \,m$ apart. If the pupil of the eye of an observer has a diameter of $2 \,mm$ and light of wavelength $5896 \,\text{Å}$ is used, what should be the maximum distance of the jeep from the observer if the two headlights are just separated?

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 $600 \,nm$.)