Q: In Young’s double-slit experiment, what is the condition for constructive interference (bright fringe) at a point on the screen?

$$\delta = d\sin\theta = m\lambda$$

Q: A laser with wavelength $$\lambda = 650\,\text{nm}$$ passes through two slits separated by $$d = 0.020\,\text{mm}. $$What is the angle $$\theta$$ for the second-order bright fringe?

$$\sin\theta = \frac{2\lambda}{d}$$

Q: In a single-slit diffraction experiment, what is the general condition for the location of dark fringes?

$$\sin\theta = m\lambda/a$$ \,\text{where}\, m = \pm1, \pm2, \pm3, ...$

Question 1

In Young’s double-slit experiment, what is the condition for constructive interference (bright fringe) at a point on the screen?

Accepted Answer

$$\delta = d\sin	heta = m\lambda$$

Question 2

Which of the following changes will decrease the spacing between fringes in a double-slit interference pattern, assuming all other variables are kept constant?

Accepted Answer

Increase the distance between the slits

Question 3

A laser with wavelength $$\lambda = 650\,	ext{nm}$$ passes through two slits separated by $$d = 0.020\,	ext{mm}. $$What is the angle $$	heta$$ for the second-order bright fringe?

Accepted Answer

$$\sin	heta = \frac{2\lambda}{d}$$

Question 4

In a single-slit diffraction experiment, what is the general condition for the location of dark fringes?

Accepted Answer

$$\sin	heta = m\lambda/a$$ \,	ext{where}\, m = \pm1, \pm2, \pm3, ...$

Question 5

A diffraction grating has $$n = 5000$$ lines per centimeter. What is the slit separation $$d$$?

Accepted Answer

$$d = \frac{1}{n}$$

Question 6

If the width of the slit in a single-slit diffraction experiment is decreased, what happens to the width of the central bright fringe?

Accepted Answer

It increases

Question 7

In a double-slit experiment, monochromatic light of wavelength $$600\,	ext{nm} is $$used. The slits are $$0.080\,	ext{mm}$$ apart and the screen is $$2.0\,	ext{m}$$ away. What is the distance between adjacent bright fringes?

Accepted Answer

$$\Delta y = \frac{\lambda L}{d}$$

Question 8

Which of the following best describes the effect of using white light instead of monochromatic light in Young’s double-slit experiment?

Accepted Answer

Colored fringes are formed, with the central maximum being white

Question 9

What is the intensity of light after passing through two polarizing filters with an angle $$	heta$$ between their axes, according to Malus’s law?

Accepted Answer

$$I = I_0$ \cos^2$	heta$$

Question 10

A diffraction grating produces sharp, narrow principal maxima. What happens to the separation between adjacent principal maxima if the number of lines per centimeter is increased?

Accepted Answer

The separation increases

Question 11

In a double-slit experiment, what is the path difference for the second dark fringe from the central maximum?

Accepted Answer

$$\delta = 1.5\lambda$$

Question 12

Which of the following is NOT a requirement for observing a stable interference pattern in Young’s double-slit experiment?

Accepted Answer

The slits must be very close together

Question 13

If the wavelength of light used in a single-slit diffraction experiment is increased, what happens to the width of the central bright fringe?

Accepted Answer

It increases

Question 14

In a double-slit experiment, if the slit separation $$d is $$doubled, what happens to the width of the central maximum?

Accepted Answer

The width is halved

Question 15

Which property of laser light makes it ideal for producing clear interference patterns?

Accepted Answer

It is coherent and monochromatic

Question 16

What happens to the intensity of light when unpolarized light passes through a single polarizing filter?

Accepted Answer

The intensity is reduced to half

Question 17

In a single-slit diffraction experiment, what is the width of the central bright fringe?

Accepted Answer

$$w = 2\frac{\lambda L}{a}$$

Question 18

Which of the following statements about polarization is correct?

Accepted Answer

Polarization occurs when the electric field oscillates in a single plane

Question 19

A third polarizer is placed between two cross-polarized filters at an angle of $$30^\circ to $$the original plane of polarization. What fraction of the original intensity $$I_0$$ gets through all three polarizers?

Accepted Answer

$$\frac{3}{16}I_0$

Wave Optics: Interference, Diffraction, and Polarization

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