Advertisements
Advertisements
प्रश्न
A parallel beam of green light of wavelength 550 nm passes through a slit of width 0.4 mm. The intensity pattern of the transmitted light is seen on a screen that is 40 cm away. What is the distance between the two first-order minima?
Advertisements
उत्तर १
Data: λ = 550 nm = 550 × 10−9 m,
a = 0.4 mm = 4 × 10−4 m
D = 40 cm = 40 × 10−2 m
`y_md = m (lambda D)/a`
∴ `y_1 d = 1 (lambda D)/a` and
`2 y_1 d = (2 lambda D)/a`
= `(2 xx 550 xx 10^-9 xx 40 xx 10^-2)/(4 xx 10^-4)`m
= 2 × 550 × 10−6
= 1100 × 10−6
= 1.100 × 10−3 m
= 1.10 mm
उत्तर २
Given:
λ = 550 nm = 550 × 10−9 m,
a = 0.4 mm = 0.4 × 10−3 m
D = 40 cm = 40 × 10−2 m
To find: Distance between two first order minima
Formula: Width of central maxima, Wc = `(2λ"D")/"a"`
Calculation:
From formula,
Wc = `(2 xx 550 xx 10^-9 xx 40 xx 10^-2)/(0.4 xx 10^-3)`
= 2 × 550 × 10−6
= 1100 × 10−6
= 1.100 × 10−3 m
= 1.10 mm
Distance between two first-order minima = Width of central maxima = 1.10 mm
Distance between two first-order minima is 1.10 mm.
संबंधित प्रश्न
Draw the sketches to differentiate between plane wavefront and spherical wavefront.
Monochromatic light of wavelength 589 nm is incident from air on a water surface. What are the wavelength, frequency and speed of (a) reflected and (b) refracted light? Refractive index of water is 1.33.
Define a wavefront.
The wavelength of light in a medium is \[\lambda = \lambda_0 /\mu,\] where \[\lambda \] is the wavelength in vacuum. A beam of red light \[\left( \lambda_0 = 720\text{ nm} \right)\] enters water. The wavelength in water is \[\lambda = \lambda_0 /\mu = 540\text{ nm.}\] To a person under water, does this light appear green?
Is it necessary to have two waves of equal intensity to study interference pattern? Will there be an effect on clarity if the waves have unequal intensity?
The speed of light depends ____________ .
The equation of a light wave is written as \[y = A \sin\left( kx - \omega t \right).\] Here, `y` represents _______ .
The inverse square law of intensity \[\left(\text{i.e. the intensity }\infty \frac{1}{r^2}\right)\] is valid for a ____________ .
The wavelength of sodium light in air is 589 nm. (a) Find its frequency in air. (b) Find its wavelength in water (refractive index = 1.33). (c) Find its frequency in water. (d) Find its speed in water.
Find the thickness of a plate which will produce a change in optical path equal to half the wavelength λ of the light passing through it normally. The refractive index of the plate is μ.
A parallel beam of white light is incident normally on a water film 1.0 × 10−4 cm thick. Find the wavelengths in the visible range (400 nm − 700 nm) which are strongly transmitted by the film. Refractive index of water = 1.33.
Plane microwaves are incident on a long slit of width 5.0 cm. Calculate the wavelength of the microwaves if the first diffraction minimum is formed at θ = 30°.
The optical path of a ray of light of a given wavelength travelling a distance of 3 cm in flint glass having refractive index 1.6 is the same as that on travelling a distance x cm through a medium having a refractive index 1.25. Determine the value of x.
Answer in brief:
In a double-slit arrangement, the slits are separated by a distance equal to 100 times the wavelength of the light passing through the slits.
- What is the angular separation in radians between the central maximum and an adjacent maximum?
- What is the distance between these maxima on a screen 50.0 cm from the slits?
Answer in brief:
The distance between two consecutive bright fringes in a biprism experiment using the light of wavelength 6000 Å is 0.32 mm by how much will the distance change if light of wavelength 4800 Å is used?
In Young’s double-slit experiment, the two coherent sources have different intensities. If the ratio of the maximum intensity to the minimum intensity in the interference pattern produced is 25:1, what is the ratio of the intensities of the two sources?
Choose the correct option:
In Young's double-slit experiment, a thin uniform sheet of glass is kept in front of the two slits, parallel to the screen having the slits. The resulting interference pattern will satisfy:
When light travels from an optically rarer medium to an optically denser medium, the speed decreases because of change in ______
Light follows wave nature because ______
Young’s double-slit experiment is carried out using green, red and blue light, one colour at a time. The fringe widths recorded are WG, WR, and WB respectively then ______
The path difference between two waves meeting at a point is (11/4)λ. The phase difference between the two waves is ______
Two vectors of the same magnitude have a resultant equal to either of the two vectors. The angle between two vectors is
Light behaves as _________.
State the theories which were proposed to explain nature of light.
