In a double-slit experiment, filters were placed in front of a white light source to investigate the effect of changing the wavelength of the light. At first, a red filter was used instead ( λ = 600 nm ) and the fringe separation was found to be 2 . 4 mm . A blue filter was then used instead ( λ = 450 nm ) . Calculate the fringe separation with the blue filter.

We know that the double-slit equation λ = ax D or λ x = a D Given, D and a Are fixed ∴ λ 1 x 1 = λ 2 x 2 or x 2 = x 1 λ 2 λ 1 Given, λ 1 = 600 nm = 6 × 10 - 7 m , λ 2 = 450 nm = 4 . 5 × 10 - 7 m , x 1 = 2 . 4 mm = 2 . 4 × 10 - 3 By putting all the known we get x 2 = 4 . 5 × 10 - 7 × 2 . 4 × 10 - 3 6 × 10 - 7 = 1 . 8 × 10 - 3 m = 1 . 8 mm Therefore, the fringe separation with the blue filter is 1 . 8 mm

In a double-slit experiment, filters were placed in front of a white light source to investigate the effect of changing the wavelength of the light. At first, a red filter was used instead ( λ = 600 nm ) and the fringe separation was found to be 2 . 4 mm . A blue filter was then used instead ( λ = 450 nm ) . Calculate the fringe separation with the blue filter.

We know that the double-slit equation λ = ax D or λ x = a D Given, D and a Are fixed ∴ λ 1 x 1 = λ 2 x 2 or x 2 = x 1 λ 2 λ 1 Given, λ 1 = 600 nm = 6 × 10 - 7 m , λ 2 = 450 nm = 4 . 5 × 10 - 7 m , x 1 = 2 . 4 mm = 2 . 4 × 10 - 3 By putting all the known we get x 2 = 4 . 5 × 10 - 7 × 2 . 4 × 10 - 3 6 × 10 - 7 = 1 . 8 × 10 - 3 m = 1 . 8 mm Therefore, the fringe separation with the blue filter is 1 . 8 mm

A student is trying to make an accurate measurement of the wavelength of green light from a mercury lamp. The wavelength $\lambda$ of this light is 546 nm . Using a double-slit of separation 0 . 50 mm , the student can see 10 clear bright fringes on a screen at a distance of 0 . 80 m from the slits. The student can measure their overall width to within ± 1 mm Using a ruler. The student then tries an alternative experiment using a diffraction grating with 3000 lines cm - 1 . The angle between the two second-order maxima can be measured to within ± 0 . 1 ° . (b) Determine the angle of the second-order maximum that the student can measure in the second experiment.

Separation of lines in grating 3000 lines cm - 1 = 1 3000 = 3 . 33 × 10 - 6 m , n = 2 By calculation, rearrange d sin θ = nλ sinθ = nλ d , By putting all the values we get sinθ = 2 × 546 × 10 - 9 3 . 33 × 10 - 6 = 0 . 328 ∴ θ = 19 . 1 ° So, θ = 19 . 1 ° But the student will measure 19 ° .

A student is trying to make an accurate measurement of the wavelength of green light from a mercury lamp. The wavelength $\lambda$ of this light is 546 nm . Using a double-slit of separation 0 . 50 mm , the student can see 10 clear bright fringes on a screen at a distance of 0 . 80 m from the slits. The student can measure their overall width to within ± 1 mm Using a ruler. The student then tries an alternative experiment using a diffraction grating with 3000 lines cm - 1 . The angle between the two second-order maxima can be measured to within ± 0 . 1 ° . (c) Based on your answers to parts a and b , suggest which experiment you think will give the more accurate value of λ .

The double slit experiment works by shooting parallel light rays from the same source, commonly a laser, at a pair of parallel openings in order to cause interference. Whereas diffraction grating provides more slits, which increases the interference between the beams. By using more slits, we get more destructive interference. The maxima on the other hand become much brighter because of increased constructive interference. This effectively increases the resolution of the experiment, making it easier to measure the distance between consecutive maxima. For the double-slit experiment, a measured width of 9 mm for 10 Fringes will give a wavelength of 562 nm . For the diffraction grating experiment, the measured second order angle of 19 ° Will give 543 nm . Hence, the diffraction grating method give the more accurate value of λ . In practice, it is also much more precise because the fringes are bright and sharp.

In a doubleslit experiment filters were placed in front of a white light source to investigate the effect of changing the wavelength of the light At first a red filter was used instead 600nm and the fringe separation was found to be 24mm A blue filter was then used instead 450nm Calculate the fringe separation with the blue filter

EASY

AS and A Level

IMPORTANT

Physics for Cambridge International AS & A Level Coursebook 3rd Edition Digital Access>Chapter 13 - Superposition of Waves>Question>Q 11

Explain how the second-order maximum arises in terms of path difference.

EASY

AS and A Level

IMPORTANT

Physics for Cambridge International AS & A Level Coursebook 3rd Edition Digital Access>Chapter 13 - Superposition of Waves>Questions>Q 12

Monochromatic light is incident normally on a diffraction grating having $3000$ lines per centimetre. The angular separation of the zeroth- and first-order maxima is found to be $10 °$ . If $λ = 580 nm$ , calculate the angle $θ$ for the second-order maximum.

EASY

AS and A Level

IMPORTANT

Physics for Cambridge International AS & A Level Coursebook 3rd Edition Digital Access>Chapter 13 - Superposition of Waves>Questions>Q 12

Monochromatic light is incident normally on a diffraction grating having $3000$ lines per centimetre. The angular separation of the zeroth- and first-order maxima is found to be $10 °$ . If $λ = 580 nm$ , calculate the angle $θ$ for the second-order maximum.

(b) Repeat the calculation of $θ$ for $n = 3, 4$ , and so on. Determine how many maxima can be seen. Explain your answer.

EASY

AS and A Level

IMPORTANT

Physics for Cambridge International AS & A Level Coursebook 3rd Edition Digital Access>Chapter 13 - Superposition of Waves>Questions>Q 13

Consider the equation $dsinθ = nλ$ . State and explain how the interference pattern would change when:

(a) The wavelength of the incident light is increased for the same grating

EASY

AS and A Level

IMPORTANT

Physics for Cambridge International AS & A Level Coursebook 3rd Edition Digital Access>Chapter 13 - Superposition of Waves>Questions>Q 13

Consider the equation $d \sin θ = n λ$ . State and explain how the interference pattern would change when:

(b) The grating is changed for one with more lines per $cm$ for the same incident light.

EASY

AS and A Level

IMPORTANT

Physics for Cambridge International AS & A Level Coursebook 3rd Edition Digital Access>Chapter 13 - Superposition of Waves>Questions>Q 14

A student is trying to make an accurate measurement of the wavelength of green light from a mercury lamp. The wavelength $\lambda$ of this light is $546 nm$ . Using a double-slit of separation $0.50 mm$ , the student can see $10$ clear bright fringes on a screen at a distance of $0.80 m$ from the slits. The student can measure their overall width to within $\pm 1 mm$

Using a ruler. The student then tries an alternative experiment using a diffraction grating with $3000$ lines ${cm}^{- 1}$ . The angle between the two second-order maxima can be measured to within $\pm 0.1 °$ .

(a) Determine the width of the $10$ fringes that the student can measure in the first experiment.

EASY

AS and A Level

IMPORTANT

Physics for Cambridge International AS & A Level Coursebook 3rd Edition Digital Access>Chapter 13 - Superposition of Waves>Questions>Q 14

A student is trying to make an accurate measurement of the wavelength of green light from a mercury lamp. The wavelength $\lambda$ of this light is $546 nm$ . Using a double-slit of separation $0.50 mm$ , the student can see $10$ clear bright fringes on a screen at a distance of $0.80 m$ from the slits. The student can measure their overall width to within $\pm 1 mm$

Using a ruler. The student then tries an alternative experiment using a diffraction grating with $3000$ lines ${cm}^{- 1}$ . The angle between the two second-order maxima can be measured to within $\pm 0.1 °$ .

(b) Determine the angle of the second-order maximum that the student can measure in the second experiment.

EASY

AS and A Level

IMPORTANT

Physics for Cambridge International AS & A Level Coursebook 3rd Edition Digital Access>Chapter 13 - Superposition of Waves>Questions>Q 14

A student is trying to make an accurate measurement of the wavelength of green light from a mercury lamp. The wavelength $\lambda$ of this light is $546 nm$ . Using a double-slit of separation $0.50 mm$ , the student can see $10$ clear bright fringes on a screen at a distance of $0.80 m$ from the slits. The student can measure their overall width to within $\pm 1 mm$

Using a ruler. The student then tries an alternative experiment using a diffraction grating with $3000$ lines ${cm}^{- 1}$ . The angle between the two second-order maxima can be measured to within $\pm 0.1 °$ .

(c) Based on your answers to parts $a$ and $b$ , suggest which experiment you think will give the more accurate value of $λ$ .

Important Questions on Superposition of Waves

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