Optics Chapter on Light and Patterns

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Questions and Answers

What is the relationship between fringe width and the distance between the slits in a double-slit experiment?

Fringe width is inversely proportional to the distance between the slits. (correct)

Fringe width remains unchanged regardless of slit separation.

Fringe width varies with the square of the distance between the slits.

Fringe width is directly proportional to the distance between the slits.

If the wavelength of light used in a Young's double-slit experiment is increased while keeping the distance between the slits the same, what happens to the fringe width?

The fringe width decreases.

The fringe width depends on the screen distance only.

The fringe width increases. (correct)

The fringe width remains the same.

What is the main characteristic of unpolarised light?

Vibrations occur in a specific direction perpendicular to propagation.

Vibrations occur symmetrically in all possible directions. (correct)

Vibrations are confined to a single direction.

Vibrations are noticeable only in the direction of propagation.

What is the effect of polarisation on the vibrations of the electric vector in light?

It produces vibrations that are asymmetrical about the direction of propagation. Signup and view all the answers

In a Young's experiment, if the entire apparatus is immersed in water, how does this affect the fringe width?

Fringe width decreases due to lower effective wavelength. Signup and view all the answers

What is the formula for calculating the optical path length (OPL)?

OPL = Geometric length × Refractive index. Signup and view all the answers

Which of the following best describes the function of a Nicol prism?

To produce and detect plane polarised light. Signup and view all the answers

How does light behave when passing through a tourmaline crystal cut parallel to its optic axis?

It is confined to vibrations in one direction. Signup and view all the answers

In a scenario where the distance between the coherent sources is 0.3 mm and the screen is 90 cm away, which of the following calculations would yield the correct wavelength?

Wavelength = Distance between dark bands × Distance to screen. Signup and view all the answers

What happens to the fringe width if the distance to the screen is increased in a double-slit experiment?

Fringe width increases. Signup and view all the answers

What type of light emerges from a tourmaline crystal after it has been polarised?

Plane polarised light. Signup and view all the answers

In a double-slit experiment, if one slit is blocked, what type of interference is exhibited?

No interference pattern is produced. Signup and view all the answers

What property does a polaroid sheet utilize to produce plane polarised light?

Selective absorption. Signup and view all the answers

Which of the following statements accurately describes the electric vector in polarised light?

The electric vector vibrates in one direction in a plane perpendicular to the propagation. Signup and view all the answers

How does the refractive index of a medium affect the wavelength of light passing through it?

Reduces the wavelength proportionately. Signup and view all the answers

Which mechanism is primarily responsible for the polarisation of light when using a polariser?

Selective absorption and transmission. Signup and view all the answers

What is the plane in which no vibration takes place called?

Plane of polarization Signup and view all the answers

What happens to the intensity of emergent light when the axes of two tourmaline crystals are perpendicular?

It decreases to zero Signup and view all the answers

When one crystal is rotated and the intensity of light remains unchanged, which component is being tested?

Vibration direction of light Signup and view all the answers

Which statement describes the relationship between the propagation of light and the plane of vibration?

They lie in the same plane Signup and view all the answers

During the experiment with two tourmaline crystals, what is the expected outcome when the second crystal's axis aligns with the first one?

Light appears colored Signup and view all the answers

What effect does rotating crystal B have on the emergent beam when it is aligned with crystal A?

It diminishes the light's intensity Signup and view all the answers

What happens to the brightness of interference pattern lines with increasing angle of diffraction?

Brightness decreases uniformly Signup and view all the answers

What does the color change of the emergent beam indicate when using a tourmaline crystal?

The light is partially polarized Signup and view all the answers

Which of the following best describes the behavior of light in a plane of vibration?

Light vibrates in a single direction Signup and view all the answers

How does the width of the central maximum relate to the slit width and wavelength?

Width is inversely proportional to the slit width Signup and view all the answers

If the wavelength of light is lowered, what happens to the width of the bright fringes in diffraction?

Width decreases Signup and view all the answers

In Fraunhofer diffraction, how does the focal length of the second lens affect the width of the central maximum?

Increasing focal length decreases the width Signup and view all the answers

What characterizes dark lines in an interference pattern?

Dark lines are perfectly dark with decreasing width Signup and view all the answers

In the context of interference and diffraction, which wavelength results in a wider central maximum?

Wavelength of red light Signup and view all the answers

When light of wavelength 6000Å is incident normally on a slit of width 24 × $10^{-5}$ cm, what is the angular position of the second minimum from the central maximum?

$30°$ Signup and view all the answers

If a slit of width $0.2$ mm is used with light of wavelength 6328Å, how does the distance of the screen affect the angular width of the central maximum?

Distance increases angular width Signup and view all the answers

What happens to the intensity of unpolarised light when it is converted into plane polarised light?

It becomes half of its original intensity. Signup and view all the answers

If the angle of incidence on a surface is 0° or 90°, how is the reflected beam characterized?

The reflected beam is always unpolarised. Signup and view all the answers

What is the relationship between the intensity of light emerging from a polariser and the angle of an analyser?

The intensity is directly proportional to the cosine of the angle. Signup and view all the answers

Given a polarising angle of 60°, what is the calculated critical angle for that medium?

35°16' Signup and view all the answers

What is the refractive index for a medium if the polarising angle is 60°?

√3 Signup and view all the answers

For a ray of light striking a glass plate at a polarising angle, how is the angle of refraction related to the polarising angle?

It is the complement of the polarising angle. Signup and view all the answers

What is the angle of polarisation for light reflecting off the surface of water with a refractive index of 1.33?

53°4' Signup and view all the answers

Why are our eyes nearly insensitive to the polarisation of light?

They are designed to perceive only unpolarised light. Signup and view all the answers

Study Notes

Optical Path Length

Optical path length is the product of the geometric length of the optical path followed by light and the refractive index of the medium through which it travels.
This essentially means the distance light travels in a vacuum that would take the same amount of time as the light travelling the actual path through the given medium.

Interference Pattern

All bright lines are equally bright and equally spaced.
All dark lines are totally dark.
Interference bands are large in number.

Diffraction Pattern

Bright lines are not equally bright, their brightness and width decrease with the angle of diffraction.
Dark lines are perfectly dark, their contrast with bright lines and width decrease with the angle of diffraction.
Diffraction bands are few in number.

Fraunhofer Diffraction

For obtaining the Fraunhofer diffraction, the focal length of the second lens is used.

Width of Central Maxima

The width of the central maxima is proportional to the wavelength of light. This means it is wider for red light and narrower for blue light.

Polarization

In unpolarised light the vibrations of the electric vector occur symmetrically in all possible directions in a plane perpendicular to the direction of propagation of light.
In Polarised light, the vibrations of the electric vector are confined to a single direction in a plane perpendicular to the direction of propagation of light.

Polariser

Tourmaline crystal filters light selectively, passing through one direction of vibration while blocking another, resulting in plane polarised light.
Nicol Prism is an optical device used for the production and detection of plane polarised light.
Polaroid is a commercially available sheet that makes use of selective absorption to produce plane polarised light.

Plane of Polarisation and Plane of Vibration:

The plane in which vibrations of the light vector and the direction of propagation lie is known as the plane of vibration.
The plane normal to the plane of vibration and in which no vibration takes place is known as the plane of Polarisation.

Experimental Demonstration of Polarization of Light

When light is passed through two tourmaline crystals, the intensity of light decreases when their axes are rotated relative to each other.
This happens because of the selective filtering properties of tourmaline crystals, which allows only certain directions of vibration to pass through.

Intensity of Polarized Light

The intensity of the light emerging from a second polaroid (analyzer) is given by I2 = I1 cos2(θ), where θ is the angle between the transmission axes of the two polaroids.

Angle of Polarisation

For a given medium, the polarising angle is given by µ = tan ip, where µ is the refractive index of the medium and ip is the polarising angle.
The critical angle for a given medium is the angle of incidence at which the refracted ray is at 90 degrees relative to the normal.

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Description

Explore the fascinating concepts of optical path length, interference, and diffraction patterns. This quiz covers essential topics like Fraunhofer diffraction and the characteristics of central maxima. Test your understanding of how light interacts with various media in this insightful optics chapter.