Q: In a double-slit experiment, the intensity at a point on the screen is $$I = I_0$ \cos^2$(\frac{\pi d \sin \theta}{\lambda}). At $$what value of $$\theta$$ does the intensity fall to $$I_0/2$?

$$\theta = \arcsin\left(\frac{\lambda}{\pi d}\arccos\left(\frac{1}{\sqrt{2}}\right)\right)$$

Q: In a double-slit experiment, the intensity at a point on the screen is zero. Which of the following conditions must be satisfied?

$$d \sin \theta = (m + 0.5) \lambda$$

Question 1

In a Young's double-slit experiment, coherent light with wavelength $$\lambda = 450 \ \mathrm{nm}$$ falls on a pair of slits separated by $$d = 0.5 \ \mathrm{mm}. If $$the screen is $$L = 2.0 \ \mathrm{m}$$ away, what is the separation between adjacent bright fringes on the screen?

Accepted Answer

$$2.4 \ \mathrm{mm}$$

Question 2

A monochromatic light of frequency $$f = 7 	imes 10$$^{14}$$ \ \mathrm{Hz} is $$incident on two narrow slits separated by $$d = 0.3 \ \mathrm{mm}. $$The interference pattern is observed on a screen $$L = 1.5 \ \mathrm{m}$$ away. What is the separation between the first-order bright fringes?

Accepted Answer

$$1.5 \ \mathrm{mm}$$

Question 3

In a double-slit experiment, the distance between the slits is $$0.25 \ \mathrm{mm}$$ and the screen is $$1.2 \ \mathrm{m}$$ away. If the wavelength of the light used is $$600 \ \mathrm{nm}$$, what is the distance between the central maximum and the first minimum?

Accepted Answer

$$1.44 \ \mathrm{mm}$$

Question 4

A double-slit experiment uses light of wavelength $$500 \ \mathrm{nm}$$ and slit separation $$0.4 \ \mathrm{mm}. $$The screen is $$2.0 \ \mathrm{m}$$ away. What is the distance from the center of the central maximum to the first minimum?

Accepted Answer

$$1.25 \ \mathrm{mm}$$

Question 5

In a double-slit experiment, what happens to the fringe separation if the wavelength of the light is doubled while keeping all other parameters constant?

Accepted Answer

The fringe separation is doubled.

Question 6

If the distance between the slits in a double-slit experiment is decreased, what is the effect on the interference pattern observed on the screen?

Accepted Answer

The fringes become more widely spaced.

Question 7

A double-slit experiment is performed with white light. What is observed on the screen?

Accepted Answer

A single bright white fringe at the center and colored fringes on either side.

Question 8

In a double-slit experiment, the intensity at a point on the screen is $$I = I_0$ \cos^2$(\frac{\pi d \sin 	heta}{\lambda}). At $$what value of $$	heta$$ does the intensity fall to $$I_0/2$?

Accepted Answer

$$	heta = \arcsin\left(\frac{\lambda}{\pi d}\arccos\left(\frac{1}{\sqrt{2}}ight)ight)$$

Question 9

A student performs a double-slit experiment and measures the distance between the central maximum and the third bright fringe to be $$6.0 \ \mathrm{mm}. If $$the screen is $$1.5 \ \mathrm{m}$$ away and the slit separation is $$0.5 \ \mathrm{mm}$$, what is the wavelength of the light used?

Accepted Answer

$$600 \ \mathrm{nm}$$

Question 10

In a double-slit experiment, if the screen is moved farther away from the slits, what happens to the fringe separation?

Accepted Answer

The fringe separation increases.

Question 11

Which of the following best explains why coherent light is necessary for observing a stable interference pattern in a double-slit experiment?

Accepted Answer

Coherent light has a constant phase relationship, ensuring constructive and destructive interference at fixed positions.

Question 12

A double-slit experiment is set up with slit separation $$d$$ and wavelength $$\lambda. If $$the order of the maximum is $$m$$, what is the path difference between the two slits for the $$m-th $$bright fringe?

Accepted Answer

$$m \lambda$$

Question 13

In a double-slit experiment, the intensity at a point on the screen is zero. Which of the following conditions must be satisfied?

Accepted Answer

$$d \sin 	heta = (m + 0.5) \lambda$$

Question 14

A double-slit experiment is performed in air and then repeated in water (refractive index $$n \u003e 1) $$with the same setup. What happens to the fringe separation?

Accepted Answer

The fringe separation decreases.

Question 15

If the intensity at the central maximum in a double-slit experiment is $$I_0$$, what is the intensity at a point where the path difference is $$\lambda/2$$?

Accepted Answer

$$0$$

Young's Double-Slit Experiment and Thin Film Interference: Study Notes

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