New chat PYQ Library Doubts Rank report

Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →

Wave Optics question

2024 · 4 Apr · Shift 2 · Q73

Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.

PYQ Library
JEE Main
Physics
Wave Optics
2024 · 4 Apr · Shift 2 · Q73

Wave Optics question

2024 · 4 Apr · Shift 2 · Q73

JEE MainPhysicsWave OpticsMCQ+4 / −1

The width of one of the two slits in a Young's double slit experiment is 4 times that of the other slit. The ratio of the maximum of the minimum intensity in the interference pattern is:

A
$1: 1$
B
$4: 1$
C
$16: 1$
D
$9: 1$

View written solutionFree

Correct answer: 25:9, NONE OF THE OPTIONS

Relate slit width to amplitude

In Young's double slit experiment, the amplitude contributed by a slit is proportional to its width.

Let the smaller slit have width $a$ . Then the larger slit has width $4a$ .

So the corresponding amplitudes are in the ratio $A_1 : A_2 = 1 : 4.$

Write expressions for maximum and minimum intensity

If the amplitudes of the two waves are $A_1$ and $A_2$ , then

Maximum intensity: $I_{\max} = (A_1 + A_2)^2$
Minimum intensity: $I_{\min} = (A_1 - A_2)^2$

Taking $A_1 = A$ and $A_2 = 4A$ ,

$I_{\max} = (A + 4A)^2 = (5A)^2 = 25A^2$

$I_{\min} = (4A - A)^2 = (3A)^2 = 9A^2$

Find the ratio

$I_{\max} : I_{\min} = 25A^2 : 9A^2 = 25:9$

Compare with the given options

The correct ratio is $\boxed{25:9}$

This is not present in the listed options.

So none of the options $A, B, C, D$ is correct.

Compare with stored correct answer

The stored correct answer is $D$ ( $9:1$ ), but the derived answer is $25:9$ .

Hence, the stored answer appears to be incorrect.

More from Wave Optics

Light emerges out of a convex lens when a source of light kept at its focus. The shape of wavefront of the light is :2024 · MCQ
In Young's double slit experiment, carried out with light of wavelength $5000 A o$ , the distance between the slits is $200 cm$ and the screen is at $x = 0 cm$ from the slits. The central maximum is at $x = 0 cm$ …2024 · Numerical
Given below are two statements : Statement I : When the white light passed through a prism, the red light bends lesser than yellow and violet. Statement II : The refractive indices are different for different wavelengths in dispersive…2024 · MCQ
In a single slit experiment, a parallel beam of green light of wavelength $0.20 mm$ passes through a slit of width $100 cm$ . The transmitted light is collected on a screen $100 cm$ away. The distance of first…2024 · Numerical
Two coherent monochromatic light beams of intensities I and $x I$ are superimposed. The difference between maximum and minimum possible intensities in the resulting beam is $x$ . The value of $x$ is …2024 · Numerical
A parallel beam of monochromatic light of wavelength $0.4 mm$ passes through single slit of width. Angular divergence corresponding to second order minima would be $\times 1 0^{- 3} rad$ …2024 · Numerical
Two slits are $1 m$ apart and the screen is located $500 nm$ away from the slits. A light of wavelength $500 nm$ is used. The width of each slit to obtain 10 maxima of the double slit pattern within the central…2024 · Numerical
In a Young's double slit experiment, the intensity at a point is $(\frac{1}{4})^{th}$ of the maximum intensity, the minimum distance of the point from the central maximum is $μ m$ .…2024 · Numerical