Wave Optics | Physics JEE previous year questions with Solutions

Q 1 :
The width of one of the two slits in a Young’s double slit experiment is 4 times that of the other slit. The ratio of the maximum to the minimum intensity in the interference pattern is [2024]

1 : 1
16 : 1
9 : 1
4 : 1

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3

4

(C) $Since, Intensity \propto width of slit (W)$

So, $I_{1} = I_{0}, I_{2} = 4 I_{0}$

$\frac{I_{\max}}{I_{\min}} = \frac{{(\sqrt{I_{1}} + \sqrt{I_{2}})}^{2}}{{(\sqrt{I_{1}} - \sqrt{I_{2}})}^{2}} = \frac{9 I_{0}}{I_{0}} = 9$

Q 2 :
In Young's double slit experiment, light from two identical sources are superimposing on a screen. The path difference between the two lights reaching at a point on the screen is 7λ/4. The ratio of intensity of fringe at this point with respect to the maximum intensity of the fringe is [2024]

$\frac{1}{4}$
$\frac{1}{3}$
$\frac{3}{4}$
$\frac{1}{2}$

1

2

3

4

(D) $Path difference, Δ x = \frac{7 λ}{4}$

$Phase difference, ϕ = \frac{2 π}{λ} Δ x = \frac{2 π}{λ} \times \frac{7 λ}{4} = \frac{7 π}{2}$

$Intensity, I = I_{\max} \cos^{2} (\frac{ϕ}{2})$

$\frac{I}{I_{\max}} = \cos^{2} (\frac{ϕ}{2}) = \cos^{2} (\frac{7 π}{2 \times 2}) = \cos^{2} (\frac{7 π}{4})$

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

Q 3 :
Two wavelengths $λ_{1}$ and $λ_{2}$ are used in Young's double slit experiment. $λ_{1}$ = 450 nm and $λ_{2}$ = 650 nm. The minimum order of fringe produced by $λ_{2}$ which overlaps with the fringe produced by $λ_{1}$ is $n$ . The value of $n$ is ____. [2024]

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(9) $m_{2} λ_{2} = m_{1} λ_{1}$

$\frac{m_{2}}{m_{1}} = \frac{λ_{1}}{λ_{2}} = \frac{450}{650} = \frac{9}{13}$

$i . e . 9^{th} maxima of λ_{2} overlaps with 13^{th} maxima of λ_{1} .$

$∴ n = 9$

Q 4 :
In Young’s double slit experiment, carried out with light of wavelength 5000 $Å$ , the distance between the slits is 0.3 mm and the screen is at 200 cm from the slits. The central maximum is at $x$ = 0 cm. The value of $x$ for the third maxima is __________ mm. [2024]

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(10) $β = \frac{λ D}{d} = \frac{5 \times 10^{- 7} \times 2}{3 \times 10^{- 4}} = \frac{10 \times 10^{- 3}}{3} m$

$For 3^{rd} maxima y_{3} = 3 β = 10 \times 10^{- 3} m = 10 mm$

Q 5 :
Two slits are 1 mm apart and the screen is located 1 m away from the slits. A light of wavelength 500 nm is used. The width of each slit to obtain 10 maxima of the double slit pattern within the central maximum of the single slit pattern is ___ × $10^{- 4}$ m. [2024]

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(2) $d = 1 m m,$ $D = 1 m,$ $λ = 500 n m$

$10 (\frac{λ D}{d}) = \frac{2 λ D}{a}$

$a = \frac{d}{5} = \frac{10 \times 10^{- 4} m}{5} = 2 \times 10^{- 4}$

Q 6 :
In a Young’s double slit experiment, the intensity at a point is ${(\frac{1}{4})}^{t h}$ of the maximum intensity. The minimum distance of the point from the central maximum is _____ µm.

(Given: $λ = 600 n m,$ $d = 1.0 m m,$ $D = 1.0 m$ ) [2024]

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

$\frac{1}{4} = \cos^{2} (\frac{Δ ϕ}{2})$

$Δ ϕ = \frac{2 π}{λ} Δ x \Rightarrow Δ ϕ = \frac{2 π}{3} = \frac{2 π}{λ} Δ x \Rightarrow Δ x = \frac{λ}{3}$

$\Rightarrow Δ x = \frac{d y}{D} = \frac{λ}{3}$

$\Rightarrow y = \frac{λ D}{3 d} = \frac{600 \times 10^{- 9} \times 1}{3 \times 10^{- 3}} = 2 \times 10^{- 4} m = 200 μ m$

Q 7 :
Monochromatic light of wavelength 500 nm is used in Young's double slit experiment. An interference pattern is obtained on a screen when one of the slits is covered with a very thin glass plate (refractive index = 1.5), the central maximum is shifted to a position previously occupied by the 4th bright fringe. The thickness of the glass plate is _____ µm. [2024]

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(4) When glass plate is inserted, then the extra path difference will be

$(μ - 1) t = n λ$

$(1.5 - 1) t = 4 \times 500 \times 10^{- 9}$

$\Rightarrow t = \frac{4 \times 500 \times 10^{- 9}}{0.5} = 4 \times 10^{- 6} m = 4 μ m$

Topic Question Set

Q 1 :
The width of one of the two slits in a Young’s double slit experiment is 4 times that of the other slit. The ratio of the maximum to the minimum intensity in the interference pattern is [2024]

Q 2 :
In Young's double slit experiment, light from two identical sources are superimposing on a screen. The path difference between the two lights reaching at a point on the screen is 7λ/4. The ratio of intensity of fringe at this point with respect to the maximum intensity of the fringe is [2024]

Q 3 :
Two wavelengths $λ_{1}$ and $λ_{2}$ are used in Young's double slit experiment. $λ_{1}$ = 450 nm and $λ_{2}$ = 650 nm. The minimum order of fringe produced by $λ_{2}$ which overlaps with the fringe produced by $λ_{1}$ is $n$ . The value of $n$ is ____. [2024]

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Q 4 :
In Young’s double slit experiment, carried out with light of wavelength 5000 $Å$ , the distance between the slits is 0.3 mm and the screen is at 200 cm from the slits. The central maximum is at $x$ = 0 cm. The value of $x$ for the third maxima is __________ mm. [2024]

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Q 5 :
Two slits are 1 mm apart and the screen is located 1 m away from the slits. A light of wavelength 500 nm is used. The width of each slit to obtain 10 maxima of the double slit pattern within the central maximum of the single slit pattern is ___ × $10^{- 4}$ m. [2024]

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Q 6 :
In a Young’s double slit experiment, the intensity at a point is ${(\frac{1}{4})}^{t h}$ of the maximum intensity. The minimum distance of the point from the central maximum is _____ µm.

(Given: $λ = 600 n m,$ $d = 1.0 m m,$ $D = 1.0 m$ ) [2024]

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Topic Question Set

Q 1 : The width of one of the two slits in a Young’s double slit experiment is 4 times that of the other slit. The ratio of the maximum to the minimum intensity in the interference pattern is [2024]

Q 3 : Two wavelengths λ1 and λ2 are used in Young's double slit experiment. λ1 = 450 nm and λ2 = 650 nm. The minimum order of fringe produced by λ2 which overlaps with the fringe produced by λ1 is n. The value of n is ____. [2024]

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Q 4 : In Young’s double slit experiment, carried out with light of wavelength 5000 Å, the distance between the slits is 0.3 mm and the screen is at 200 cm from the slits. The central maximum is at x = 0 cm. The value of x for the third maxima is __________ mm. [2024]

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Q 5 : Two slits are 1 mm apart and the screen is located 1 m away from the slits. A light of wavelength 500 nm is used. The width of each slit to obtain 10 maxima of the double slit pattern within the central maximum of the single slit pattern is ___ × 10-4 m. [2024]

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Q 6 : In a Young’s double slit experiment, the intensity at a point is (14)thof the maximum intensity. The minimum distance of the point from the central maximum is _____ µm. (Given: λ=600nm, d=1.0mm, D=1.0m) [2024]

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Q 1 :
The width of one of the two slits in a Young’s double slit experiment is 4 times that of the other slit. The ratio of the maximum to the minimum intensity in the interference pattern is [2024]

Q 3 :
Two wavelengths $λ_{1}$ and $λ_{2}$ are used in Young's double slit experiment. $λ_{1}$ = 450 nm and $λ_{2}$ = 650 nm. The minimum order of fringe produced by $λ_{2}$ which overlaps with the fringe produced by $λ_{1}$ is $n$ . The value of $n$ is ____. [2024]

Q 4 :
In Young’s double slit experiment, carried out with light of wavelength 5000 $Å$ , the distance between the slits is 0.3 mm and the screen is at 200 cm from the slits. The central maximum is at $x$ = 0 cm. The value of $x$ for the third maxima is __________ mm. [2024]

Q 5 :
Two slits are 1 mm apart and the screen is located 1 m away from the slits. A light of wavelength 500 nm is used. The width of each slit to obtain 10 maxima of the double slit pattern within the central maximum of the single slit pattern is ___ × $10^{- 4}$ m. [2024]

Q 6 :
In a Young’s double slit experiment, the intensity at a point is ${(\frac{1}{4})}^{t h}$ of the maximum intensity. The minimum distance of the point from the central maximum is _____ µm.

(Given: $λ = 600 n m,$ $d = 1.0 m m,$ $D = 1.0 m$ ) [2024]