Optics Chapter - Physics JEE Main

JEE Main Physics Chapters 

1

Units and Measurement

11

Electrostatics

2

Kinematics

12

Current Electricity

3

Laws of Motion

13

Magnetic Effects of Current and Magnetism

4

Work, Energy and Power

14

Electromagnetic Induction and Alternating Currents

5

Rotational Motion

15

Electromagnetic Waves

6

Gravitation

16

Optics

7

Properties of Solids and Liquids

17

Dual Nature of Matter

8

Thermodynamics

18

Atoms and Nuclei

9

Kinetic Theory of Gases

19

Electronic Devices

10

Oscillations and Waves

20

Communication Systems

Name of the Concept

Key Points of the Concepts

1. Reflection of light

• The phenomenon of light reflection is the change in the course of light without any change in the medium.

• The mirror formula is a relationship between the mirror's focal length and the distance between the object and image from the mirror.

• Magnification is defined as the ratio of the size of the image formed by the mirror to the size of the object. 

2. Refraction of light

• Refraction of light is the phenomenon of change in the path of light when it goes from one medium to another.

• The basic cause of refraction is change in the velocity of light when it goes from one medium to the other.

• The phenomenon of total internal reflection is the reflection of light into a denser medium from an interface of this denser medium and a rarer medium.

• Spherical reflecting surfaces is a part of a sphere of transparent medium and these are of two types:

1. Convex spherical refracting surface, which is convex towards the rarer medium side. 

2. Concave  spherical refracting surface, which is concave towards the rarer medium side.

• A lens is a section of a transparent refracting material that is joined by two spherical surfaces or one spherical surface and one plane surface. There are types of lenses:

1. Converging or Convex lens

2. Diverging or Concave lens

• Lens maker’s formula is a relation that connects focal length($f$) of the lens to radii of curvature ($R_1$ and $R_2$) of the two surfaces of the lens and refractive index($\mu$) of the material of the lens. It is written as

$\dfrac{1}{f}=(\mu-1)(\dfrac{1}{R_1}-\dfrac{1}{R_2})$

• Power of a lens ($P$) is defined as the ability of the lens to converge a beam of light falling on the lens and it is measured as

 $P=\dfrac{1}{f}$

• Combination of Thin Lenses in Contact: When two or more thin lenses are in contact, they can be treated as a single lens. The power of the combination is the sum of the individual powers of the lenses.

3. Dispersion of light

• The phenomenon of light dispersion is the splitting of a white light beam into its constituent colours when it passes through a prism.

• The ratio of angular dispersion to the mean deviation generated by a prism is known as its dispersive power.

• The dispersive power of a prism is solely determined by the type of prism material. However, angular dispersion and mean deviation, both depend on angle of prism in addition to the nature of material of the prism.

4. Deviation and Dispersion of Light by a Prism

• A prism is a triangular optical element that refracts light, causing it to deviate. The deviation is different for different colors due to dispersion, and this phenomenon is key in understanding how rainbows form and how prisms split white light into its constituent colors.

5. Optical instruments

• A simple microscope is used for observing magnified images of tiny objects and it consists of a converging lens of small focal length.

• Magnifying power ($m$) of a simple microscope is defined as the ratio of angles subtended by the image and the object on the eye, when both are at the least distance of distinct vision($d$) from the eye. It is given as

$m=(1+\dfrac{d}{f})$

• Compound microscope consists of two lenses co-axially at the free end of a tube, at a suitable fixed distance from each other.

• The magnifying power of the compound microscope is given as

$m=\dfrac{L}{|f_o|}(1+\dfrac{d}{f_e})$

Here, $f_o$= focal length of objective lens, $f_e$= focal length of the eye-piece, $L$= length of the microscope tube and $d$= least distance of distinct vision.

• Astronomical telescope consists of two lenses i.e, an objective lens which is of large focal length($f_o$) and an eyepiece which has a small focal length($f_e$).

• The astronomical telescope's magnification power is given as

$m=\dfrac{f_o}{-f_e}$

• Reflecting type of telescope consists of a parabolic concave reflector with a narrow hole at the centre and secondary convex mirror.

• In normal adjustment, magnifying power of the a reflecting type telescope is given as

$m=\dfrac{R/2}{f_e}$

Here, $R$= radius of curvature of concave reflector and $f_e$ = focal length of the eyepiece

• Refracting Telescope employs lenses to bend and focus light. The Keplerian telescope is a well-known example.

6. Huygens principle and interference of light

• The continuous location of all particles of a material vibrating in the same phase is characterised as a wave front.

• According to Huygen’s principle,

1. Every particle on the given wavefront acts as a fresh source of new disturbance, called secondary wavelets, which travels in all directions with the velocity of light in the medium.

2. At any instant, a surface encountering these secondary wavelets tangentially in the forward direction yields the new wavefront at that instant. This is referred to as a secondary wave front.

• The process of redistribution of light energy in a medium caused by the superposition of light waves from two coherent sources is known as interference of light.

• Condition for constructive interference:

$x=n\lambda$

Here, $x$= path difference between two waves, $\lambda$= wavelength of light and $n$= 0,1,2……..

• Condition for destructive interference:

$x=\dfrac{(2n-1)\lambda}{2}$

Here, $n$ = 1,2,3………….

• In Young’s double slit experiment,

1. The condition for bright fringe is given as

$x=n\lambda(\dfrac{D}{d})$

Here, $n$ = 0,1,2,3………

2. The condition for dark fringe is

$x=(2n-1)\dfrac{\lambda}{2}\dfrac{D}{d}$

Here, $D$= distance between slit and screen, $d$ = distance between two slits and $n$ = 1,2,3……….

3. The expression of fringe width ($\beta$) is

$\beta=\dfrac{\lambda D}{d}$

7. Diffraction and polarisation of light

• The phenomenon of light bending around corners of a barrier or aperture in its path is known as diffraction.

• The $n^{th}$ secondary minima is given as

$\sin\theta_n=\dfrac{n\lambda}{a}$

• The $n^{th}$ secondary maxima is given as

$\sin\theta_n=\dfrac{(2n+1)\lambda}{2a}$

Here, $n$ = 1,2,3……an integer, $a$ = width of the aperture, $\theta$ = angle made by secondary waves while travelling and $\lambda$ = wavelength of light.

• The phenomenon of restricting the vibration of light in a particular direction, perpendicular to the direction of the wave motion, is called polarisation of light.

• According to the Law of Malus, when a beam of completely polarised light is incident on an analyser, the resultant intensity of light ($I$) transmitted from the analyser varies directly as the square of the cosine of the angle ($\theta$) between plane of transmission of analyser and polariser.

8. Coherent Sources and Sustained Interference

• For interference to occur, the sources of light must be coherent, meaning they have a constant phase relationship. Coherent sources are essential for sustained interference patterns. These patterns play a crucial role in applications such as interferometry and the study of thin films.

9. Diffraction and the Width of Central Maximum

• Diffraction is a phenomenon where light waves bend around obstacles and spread out. When light passes through a single slit, it diffracts, leading to the formation of a diffraction pattern. The width of the central maximum in a single-slit diffraction pattern can be determined using the formula:

W= 2λL/w

Where:

• λ is the wavelength of light.

• L is the distance from the slit to the screen.

• w is the width of the slit.

10. Resolving Power of Microscopes and Astronomical Telescopes

• The resolving power of optical instruments like microscopes and telescopes is a critical factor. It determines their ability to distinguish two closely spaced objects. The resolving power of a microscope or a telescope can be defined as:

R= 1.22λ/D

Where:

• λ is the wavelength of light.

• D is the diameter of the objective lens or mirror.

11. Polarization and Brewster's Law

• Polarization is the phenomenon where light waves vibrate in a specific direction. Brewster's Law helps us understand the angle at which polarized light is reflected from a surface. It is expressed as:

$\tan \theta_B = \dfrac{n_2}{n_1}$

Where:

• $\theta_B$ is the Brewster angle.

• n₁ and n₂ are the refractive indices of the two mediums.

12. Uses of Plane-Polarized Light and Polaroids

• Polarized light has numerous applications, including glare reduction, 3D cinema, and stress analysis. 

• Polaroid filters, which selectively transmit polarized light, are commonly used to achieve these effects.

S.No.

Name of the Concept

Formula

Reflection of light

• Mirror formula:

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

• Linear magnification of a spherical mirror

$m=-\dfrac{v}{u}$

Refraction of light

• Snell’s Law:

$\frac{\mu_2}{\mu_1}=\frac{\sin i}{\sin r}$

Here, $\mu_1$ and $\mu_1$ are the refractive indices of the medium 1 and medium 2.

• Total internal reflection:

$\mu^a_w=\frac{1}{\sin C}$

• Lens maker’s formula:

$\frac{1}{f}=(\mu-1)(\frac{1}{R_1}-\frac{1}{R_2})$

• Magnification for concave lens:

$m=\frac{v}{u}$

• Equivalent focal length ($F$) of two lenses having focal lengths $f_1$, $f_2$ and separated by a distance $d$ is

$\frac{1}{F}=\frac{1}{f_1}+\frac{1}{f_2}-\frac{d}{f_1f_2}$

Dispersion of light

• Refractive index of prism is

$\mu=\frac{\sin(A+\delta_m/2)}{\sin (A/2)}$

Here, $A$ = angle of prism and $\delta_m$ = minimum deviation angle.

• Dispersive power ($\omega$) is given as

$\omega=\frac{d\mu}{\mu-1}$

Here, $d\mu$ = difference in refractive indices of prism for violet and red colour.

Optical instruments

• A simple microscope's magnification power ($m$) equals to

$m=(1+\frac{d}{f})$

• The magnifying power of compound microscope is

$m=\frac{L}{|f_o|}(1+\frac{d}{f_e})$

• Magnifying power of astronomical telescope is

$m=\frac{f_o}{-f_e}$

• Magnifying power of the a reflecting type telescope is

$m=\frac{R/2}{f_e}$

Huygens Principle and interference of light

• In Young’s double slit experiment, the condition for bright fringe is given as

$x=n\lambda(\frac{D}{d})$

Here, $n$ = 0,1,2,3………

• The condition for dark fringe is

$x=(2n-1)\frac{\lambda}{2}\frac{D}{d}$

Here, $n$ = 1,2,3……….

• Fringe width ($\beta$) is

$\beta=\frac{\lambda D}{d}$

6.

Diffraction and polarisation of light

• The $n^{th}$ secondary minima in diffraction is

$\sin\theta_n=\frac{n\lambda}{a}$

• The $n^{th}$ secondary maxima in diffraction is

$\sin\theta_n=\frac{(2n+1)\lambda}{2a}$

• Law of Malus is

$I\varpropto\cos^2\theta$

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