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Chapter 18: Problem 165

The maximum number of possible interference maximum for slit separation equal to twice the wavelength in Young's double-slit experiment is [2004] (A) Three (B) Five (C) Infinite (D) Zero

Short Answer

Expert verified
The maximum number of possible interference maximum for slit separation equal to twice the wavelength in Young's double-slit experiment is \( (A) \text{ Three} \), as our analysis with the interference maximum formula shows that there are three possible values of 胃 corresponding to maximum intensity.

Step by step solution

01

Understand Young's Double-Slit Experiment

In Young's double-slit experiment, light passes through two narrow slits separated by a distance d, creating an interference pattern on a screen positioned along the path of the light. The interference pattern consists of bright and dark fringes, which are regions of maximum and minimum intensity, respectively. The maximum intensity (bright) fringes occur when the path difference between the waves from the two slits is a multiple of the wavelength of the light.
02

Identify the Formula for Interference Maximum

The formula for finding the position of the interference maximum in a double-slit experiment is given by: \( n\lambda = d \sin\theta \) where: - n is an integer (0, 1, 2, 3, ...) - 位 (lambda) is the wavelength of the light - d is the separation between the slits - 胃 (theta) is the angle between the path of the light from the center of the slits and the position of the maximum intensity fringe on the screen
03

Evaluate the Condition Given in the Problem

The problem states that the slit separation d is equal to twice the wavelength (2位). We can substitute this into the formula for the interference maximum: \( n\lambda = (2\lambda) \sin\theta \)
04

Simplify the Equation and Analyze the Variations of 胃

Divide both sides of the equation by 位: \( n = 2 \sin\theta \) Now, we need to analyze the possible values of n and the corresponding 胃 values to determine the maximum number of interference maximums. Since 胃 is an angle in a sine function, its value ranges from -1 to 1. For n = 0: \( 0 = 2 \sin\theta \) => \(\sin\theta = 0 \) For n = 1: \( 1 = 2 \sin\theta \) => \(\sin\theta = \frac{1}{2} \) For n = 2: \( 2 = 2 \sin\theta \) => \(\sin\theta = 1 \) For n = 3: \( 3 = 2 \sin\theta \) This value of n is impossible because the maximum value of \(\sin\theta\) is 1. This shows that the maximum value for n is 2, which corresponds to three possible values of 胃 with interference maximums.
05

Choose the Correct Answer

As our analysis demonstrated, the maximum number of interference maximums in this condition is three. So, the correct answer is (A) Three.

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Most popular questions from this chapter

In YDSE distance between the slits plane and screen is \(1 \mathrm{~m}\) and distance between two slits is \(5 \mathrm{~mm}\). If slabs of thickness \(2 \mathrm{~mm}\) and \(1.5 \mathrm{~mm}\) having refractive index \(1.5\) and \(1.4\) are placed in front of two slits, the shift of central maximum will be (A) \(2 \mathrm{~m}\) (B) \(8 \mathrm{~cm}\) (C) \(20 \mathrm{~cm}\) (D) \(80 \mathrm{~cm}\)

Two polaroids are kept crossed to each other. Now one of them is rotated through an angle of \(45^{\circ}\). The percentage of unpolarized incident light now transmitted through the system is (A) \(15 \%\) (B) \(25 \%\) (C) \(50 \%\) (D) \(60 \%\)

Two convex lenses placed in contact form the image of a distant object at \(P\). If the lens \(B\) is moved to the right, the image will (A) move to the left. (B) move to the right. (C) remain at \(P\). (D) move either to the left or right, depending upon focal lengths of the lenses.

Light of wavelength \(6328 \AA\) is incident normally on a slit having a width of \(0.2 \mathrm{~mm}\). The width of the central maximum measured from minimum to minimum of diffraction pattern on a screen \(9.0\) metres away will be about (A) \(0.36^{\circ}\) (B) \(0.18^{\circ}\) (C) \(0.72^{\circ}\) (D) \(0.09^{\circ}\)

A ray of light strikes a glass plate at an angle of \(60^{\circ}\) with the vertical. If the reflected and refracted rays are perpendicular to each other, the refractive index of glass is (A) \(\frac{\sqrt{3}}{2}\) (B) \(\frac{3}{2}\) (C) \(\frac{1}{2}\) (D) \(\sqrt{3}\)
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