Wave Optics | Physics JEE previous year questions with Solutions

Q 1 :
A monochromatic light of wavelength 6000 $Å$ is incident on the single slit of width 0.01 mm. If the diffraction pattern is formed at the focus of the convex lens of focal length 20 cm, the linear width of the central maximum is [2024]

60 mm
24 mm
120 mm
12 mm

1

2

3

4

(B) $Angular width = \frac{2 λ}{a}$

$Linear width = \frac{2 λ}{a} \cdot f$

$= \frac{2 \times 6000 \times 10^{- 10} \times 20 \times 10^{- 2}}{0.01 \times 10^{- 3}}$

$= 24 \times 10^{- 3} m = 24 mm$

Q 2 :
A microwave of wavelength 2.0 cm falls normally on a slit of width 4.0 cm. The angular spread of the central maxima of the diffraction pattern obtained on a screen 1.5 m away from the slit will be [2024]

30°
15°
60°
45°

1

2

3

4

(C) $d \sin θ = λ (Half angular speed)$

$\sin θ = \frac{λ}{d} = \frac{2 \times 10^{- 2}}{4 \times 10^{- 2}} = \frac{1}{2} \Rightarrow θ = 30 °$

$Full angular speed = 2 θ = 60 °$

Q 3 :
A parallel beam of monochromatic light of wavelength 600 nm passes through a single slit of 0.4 mm width. Angular divergence corresponding to the second order minima would be ____ × $10^{- 3}$ rad. [2024]

0%

(6) $\sin θ ≃ θ ≃ \frac{2 λ}{b}$

$= \frac{2 \times 600 \times 10^{- 9}}{4 \times 10^{- 4}} = 3 \times 10^{- 3} rad$

Total divergence = $(3 + 3) \times 10^{- 3} = 6 \times 10^{- 3} r a d$

Q 4 :
A parallel beam of monochromatic light of wavelength 5000 $Å$ is incident normally on a single narrow slit of width 0.001 mm. The light is focused by a convex lens on the screen, placed on its focal plane. The first minima will be formed for the angle of diffraction of ____ (degree). [2024]

0%

(30) For first minima

$a \sin θ = λ$

$\Rightarrow \sin θ = \frac{λ}{a} = \frac{5000 \times 10^{- 10}}{1 \times 10^{- 6}} = \frac{1}{2}$

$\Rightarrow θ = 30 °$

Q 5 :
The diffraction pattern of a light of wavelength 400 nm diffracting from a slit of width 0.2 mm is focused on the focal plane of a convex lens of focal length 100 cm. The width of the 1st secondary maxima will be [2024]

2 mm
2 cm
0.02 mm
0.2 mm

1

2

3

4

(1)

$width of secondary maxima = \frac{λ f}{a}$

$= \frac{400 \times 10^{- 9} \times 1}{0.2 \times 10^{- 3}} = \frac{2 \times 10^{- 7}}{10^{- 4}} = 2 \times 10^{- 3} m = 2 mm$

Q 6 :
In a single slit experiment, a parallel beam of green light of wavelength 550 nm passes through a slit of width 0.20 nm. The transmitted light is collected on a screen 100 cm away. The distance of first order minima from the central maximum will be $x \times 10^{- 5}$ m. The value of $x$ is _____. [2024]

0%

(275)

$λ = 550 nm$

$D = 100 cm$

$a = 0.20 mm$

$y = \frac{D λ}{a} = \frac{100 \times 10^{- 2} \times 550 \times 10^{- 9}}{0.2 \times 10^{- 3}} = 275$

Q 7 :
In a single slit diffraction pattern, a light of wavelength 6000 $Å$ is used. The distance between the first and third minima in the diffraction pattern is found to be 3 mm when the screen is placed 50 cm away from the slits. The width of the slit is ____ $\times 10^{- 4}$ m. [2024]

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(2)

For $n^{t h}$ minima $b \sin θ = n λ$

( $λ$ is small so sin $θ$ is small, hence b tan $θ$ = $n λ$ )

$b \tan θ = n λ$

$b \frac{y}{D} = n λ$

$\Rightarrow y_{n} = \frac{n λ D}{b}$ (Position of $n^{t h}$ minima)

$B \to 1^{s t}$ minima, $A \to 3^{r d}$ minima

$y_{3} = \frac{3 λ D}{b}, y_{1} = \frac{λ D}{b}$

$Δ y = y_{3} - y_{1} = \frac{2 λ D}{b}$

$3 \times 10^{- 3} = \frac{2 \times 6000 \times 10^{- 10} \times 0.5}{b}$

$b = \frac{2 \times 6000 \times 10^{- 10} \times 0.5}{3 \times 10^{- 3}} = 2 \times 10^{- 4} m$

$x = 2$

Topic Question Set

Q 1 :
A monochromatic light of wavelength 6000 $Å$ is incident on the single slit of width 0.01 mm. If the diffraction pattern is formed at the focus of the convex lens of focal length 20 cm, the linear width of the central maximum is [2024]

Q 2 :
A microwave of wavelength 2.0 cm falls normally on a slit of width 4.0 cm. The angular spread of the central maxima of the diffraction pattern obtained on a screen 1.5 m away from the slit will be [2024]

Q 3 :
A parallel beam of monochromatic light of wavelength 600 nm passes through a single slit of 0.4 mm width. Angular divergence corresponding to the second order minima would be ____ × $10^{- 3}$ rad. [2024]

0%

Q 4 :
A parallel beam of monochromatic light of wavelength 5000 $Å$ is incident normally on a single narrow slit of width 0.001 mm. The light is focused by a convex lens on the screen, placed on its focal plane. The first minima will be formed for the angle of diffraction of ____ (degree). [2024]

0%

Q 5 :
The diffraction pattern of a light of wavelength 400 nm diffracting from a slit of width 0.2 mm is focused on the focal plane of a convex lens of focal length 100 cm. The width of the 1st secondary maxima will be [2024]

0%

Q 7 :
In a single slit diffraction pattern, a light of wavelength 6000 $Å$ is used. The distance between the first and third minima in the diffraction pattern is found to be 3 mm when the screen is placed 50 cm away from the slits. The width of the slit is ____ $\times 10^{- 4}$ m. [2024]

0%

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Topic Question Set

Q 1 : A monochromatic light of wavelength 6000 Å is incident on the single slit of width 0.01 mm. If the diffraction pattern is formed at the focus of the convex lens of focal length 20 cm, the linear width of the central maximum is [2024]

Q 2 : A microwave of wavelength 2.0 cm falls normally on a slit of width 4.0 cm. The angular spread of the central maxima of the diffraction pattern obtained on a screen 1.5 m away from the slit will be [2024]

Q 3 : A parallel beam of monochromatic light of wavelength 600 nm passes through a single slit of 0.4 mm width. Angular divergence corresponding to the second order minima would be ____ × 10-3 rad. [2024]

0%

Q 4 : A parallel beam of monochromatic light of wavelength 5000Å is incident normally on a single narrow slit of width 0.001 mm. The light is focused by a convex lens on the screen, placed on its focal plane. The first minima will be formed for the angle of diffraction of ____ (degree). [2024]

0%

Q 5 : The diffraction pattern of a light of wavelength 400 nm diffracting from a slit of width 0.2 mm is focused on the focal plane of a convex lens of focal length 100 cm. The width of the 1st secondary maxima will be [2024]

Q 6 : In a single slit experiment, a parallel beam of green light of wavelength 550 nm passes through a slit of width 0.20 nm. The transmitted light is collected on a screen 100 cm away. The distance of first order minima from the central maximum will be x×10-5m. The value of x is _____. [2024]

0%

Q 7 : In a single slit diffraction pattern, a light of wavelength 6000Å is used. The distance between the first and third minima in the diffraction pattern is found to be 3 mm when the screen is placed 50 cm away from the slits. The width of the slit is ____×10-4m. [2024]

0%

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Q 1 :
A monochromatic light of wavelength 6000 $Å$ is incident on the single slit of width 0.01 mm. If the diffraction pattern is formed at the focus of the convex lens of focal length 20 cm, the linear width of the central maximum is [2024]

Q 2 :
A microwave of wavelength 2.0 cm falls normally on a slit of width 4.0 cm. The angular spread of the central maxima of the diffraction pattern obtained on a screen 1.5 m away from the slit will be [2024]

Q 3 :
A parallel beam of monochromatic light of wavelength 600 nm passes through a single slit of 0.4 mm width. Angular divergence corresponding to the second order minima would be ____ × $10^{- 3}$ rad. [2024]

Q 4 :
A parallel beam of monochromatic light of wavelength 5000 $Å$ is incident normally on a single narrow slit of width 0.001 mm. The light is focused by a convex lens on the screen, placed on its focal plane. The first minima will be formed for the angle of diffraction of ____ (degree). [2024]

Q 5 :
The diffraction pattern of a light of wavelength 400 nm diffracting from a slit of width 0.2 mm is focused on the focal plane of a convex lens of focal length 100 cm. The width of the 1st secondary maxima will be [2024]

Q 7 :
In a single slit diffraction pattern, a light of wavelength 6000 $Å$ is used. The distance between the first and third minima in the diffraction pattern is found to be 3 mm when the screen is placed 50 cm away from the slits. The width of the slit is ____ $\times 10^{- 4}$ m. [2024]