Wave Optics | Physics JEE previous year questions with Solutions

Q 21 :

The width of fringe is 2 mm on the screen in a double slits experiment for the light of wavelength of 400 nm. The width of the fringe for the light of wavelength 600 nm will be ________ [2023]

4 mm
1.33 mm
2 mm
3 mm

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(4)

$Fringe width (β) = \frac{D λ}{d}$

$\Rightarrow \frac{β_{2}}{β_{1}} = \frac{λ_{2}}{λ_{1}}$

$\Rightarrow \frac{β_{2}}{2 mm} = \frac{600 nm}{400 nm} = \frac{3}{2}$

$\Rightarrow β_{2} = 3 mm$

Q 22 :

In Young's double slit experiment, two slits $S_{1}$ and $S_{2}$ are $' d'$ distance apart and the separation from slits to screen is $D$ (as shown in figure). Now if two transparent slabs of equal thickness 0.1 mm but refractive index 1.51 and 1.55 are introduced in the path of beam $(λ = 4000 Å)$ from $S_{1}$ and $S_{2}$ respectively. The central bright fringe spot will shift by _______ number of fringes. [2023]

0%

(10)

$Path difference at P be Δ x$

$Δ x = (μ_{2} - μ_{1}) t = (1.55 - 1.51) 0.1 mm = 0.04 \times 10^{- 4}$

$Δ x = 4 \times 10^{- 6} = 4 μ m$

$y = \frac{Δ x D}{d} = 4 \times 10^{- 6} \frac{D}{d}$

$[y is the distance of central maxima from geometric center]$

$Fringe width = \frac{λ D}{d} = 4 \times 10^{- 6} m \frac{D}{d} = 4 μ m \frac{D}{d}$

$∴$ $Central bright fringe spot will shift by' x'$

$Number of shift = \frac{y}{β} = \frac{4 \times 10^{- 6} D / d}{4 \times 10^{- 7} D / d} = 10$

Q 23 :

In a Young's double slit experiment, the intensities at two points, for the path difference $\frac{λ}{4}$ and $\frac{λ}{3}$ ( $λ$ being the wavelength of light used) are $I_{1}$ and $I_{2}$ respectively. If $I_{0}$ denotes the intensity produced by each one of the individual slits, then $\frac{I_{1} + I_{2}}{I_{0}} =$ ________ . [2023]

0%

(3)

$I = 4 I_{0} \cos^{2} (\frac{Δ ϕ}{2})$

$I_{1} = 4 I_{0} \cos^{2} (\frac{π}{4}) = 2 I_{0}$

$I_{2} = 4 I_{0} \cos^{2} (\frac{2 π}{3}) = I_{0}$

$\Rightarrow \frac{I_{1} + I_{2}}{I_{0}} = 3$

Q 24 :

Two light waves of wavelengths 800 and 600 nm are used in Young’s double slit experiment to obtain interference fringes on a screen placed 7 m away from plane of slits. If the two slits are separated by 0.35 mm, then shortest distance from the central bright maximum to the point where the bright fringes of the two wavelength coincide will be ________ mm. [2023]

0%

(48)

$ω_{1} = \frac{λ_{1} D}{d} and ω_{2} = \frac{λ_{2} D}{d}$

$ω_{1} = 16 mm and ω_{2} = 12 mm$

$so LCM (ω_{1}, ω_{2}) = 48 mm$

$so at 48 mm distance both bright fringes will be found.$

Q 25 :

As shown in the figure, in Young's double slit experiment, a thin plate of thickness $t = 10 μ m$ and refractive index $μ = 1.2$ is inserted infront of slit $S_{1}$ . The experiment is conducted in air ( $μ = 1$ ) and uses a monochromatic light of wavelength $λ = 500 nm$ . Due to the insertion of the plate, central maxima is shifted by a distance of $x β_{0}$ . $β_{0}$ is the fringe-width before the insertion of the plate. The value of the $x$ is ________ . [2023]

0%

(4)

$Fringe shift S = \frac{t (μ - 1)}{λ} β_{0}$

$= \frac{10 \times 10^{- 6} (1.2 - 1)}{5 \times 10^{- 7}} β_{0} = x β_{0}$

$\Rightarrow x = \frac{10^{- 5} \times 0.2}{5 \times 10^{- 7}} = 4$

Q 26 :

A beam of light consisting of two wavelengths 7000 $Å$ and 5500 $Å$ is used to obtain interference pattern in Young's double slit experiment. The distance between the slits is 2.5 mm and the distance between the plane of slits and the screen is 150 cm. The least distance from the central fringe, where the bright fringes due to both the wavelengths coincide, is $n \times 10^{- 5} m$ . The value of $n$ is _______. [2023]

0%

(462)

$d = 2.5 mm, D = 150 cm$

$Fringe width β = \frac{λ D}{d}$

$Let n^{th} bright fringe of λ_{1} match with m^{th} bright fringe of λ_{2}$

$\Rightarrow n β_{1} = m β_{2}$

$\Rightarrow n λ_{1} = m λ_{2} \Rightarrow \frac{n}{m} = \frac{λ_{2}}{λ_{1}} = \frac{5500}{7000}$

$\Rightarrow \frac{n}{m} = \frac{11}{14}$

$Distance where bright fringe will match$

$= n β_{1} = \frac{11 \times 7000 Å \times 150 cm}{0.25 cm} = 462 \times 10^{- 5}$

Q 27 :

In two separate Young’s double-slit experimental set-ups, two monochromatic light sources of different wavelengths are used to get fringes of equal width. The ratios of the slit separations and that of the wavelengths of light used are 2 : 1 and 1 : 2 respectively. The corresponding ratio of the distances between the slits and the respective screens $(D_{1} / D_{2})$ is __________ . [2026]

0%

(4)

Q 28 :

In a double slit experiment the distance between the slits is 0.1 cm and the screen is placed at 50 cm from the slits plane. When one slit is covered with a transparent sheet having thickness t and refractive index n (= 1.5), the central fringe shifts by 0.2 cm. The value of t is __________ cm. [2026]

$6.0 \times 10^{- 3}$
$5.6 \times 10^{- 4}$
$8 \times 10^{- 4}$
$8 \times 10^{- 4}$

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(3)

$d \sin θ = (μ - 1) t$

$d [\frac{x}{D}] = (μ - 1) t$

$t = \frac{x d}{D (μ - 1)}$

$= \frac{(0.2) (0.1)}{50 (1.5 - 1)}$

$t = 8 \times 10^{- 4} cm$

Q 29 :

A beam of light consisting of wavelengths 650 nm and 550 nm illuminates the Young’s double slits with separation of 2 mm such that the interference fringes are formed on a screen, placed at a distance of 1.2 m from the slits. The least distance of a point from the central maximum, where the bright fringes due to both the wavelengths coincide, is ________ $\times 10^{- 5}$ [2026]

0%

429

Q 30 :

In the Young's double slit experiment the intensity produced by each one of the individual slits is $I_{o}$ . The distance between two slits is 2 mm. The distance of screen from slits is 10 m. The wavelength of light is $6000$ $Å$ . The intensity of light on the screen in front of one of the slits is _________ . [2026]

$4 I_{o}$
$\frac{I_{o}}{2}$
$2 I_{o}$
$I_{o}$

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(4)

Topic Question Set

Q 21 :

The width of fringe is 2 mm on the screen in a double slits experiment for the light of wavelength of 400 nm. The width of the fringe for the light of wavelength 600 nm will be ________ [2023]

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