Wave Optics is a part of JEE Main syllabus which involves some important formulae that help the students gain optimum marks. It is one of the most important chapters of Physics which is usually liked by the students and also covers a broad portion of JEE Main Syllabus.

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Wave Optics is a branch of optics that includes various phenomena such as Young’s double-slit experiment, interference pattern, the polarization of the light, and many others. It involves the study of light. This section is also called as Physic Optics because it deals with the behavior of light and its wave characteristics. Thus, wave optics can be known as a branch of physics which tackles the patterns and behaviors of light in terms of refraction or reflection.

• The topic of Wave Optics usually covers four to eight marks in the JEE Main examination.
• This topic is generally taught to the students from class 9th making it easy to understand
• Wave Optics is a section that must be covered by all the students to obtain better marks in JEE Main examination.

Laws of Reflection (reflection at the plane surface)

• All the rays that are the reflected ray, the incident ray and the normal to the reflecting surface, lie at a plane and that plane is perpendicular to the reflecting surface.
• The angle of reflection is equal to the angle of incidence and vice - versa. Therefore, angle i = angle r .

Refraction of Light

• When the wave of a light going from one medium to another medium experiences a change in its velocity, it is referred to as the refraction of the light.
• Under refraction, the sine of the angle between the incident ray and the normal ray has a constant ratio to that of the sine of the angle between the refracted ray and that of the normal ray.

sin i / sin r = v1 / v2 = 1µ2 = constant

• Now, here v1 and v2 refer to the velocities of the sound in the first and second medium respectively.
• 1µ2 refers to the refractive index of the second medium in contrast to the first.

Huygens Principle

• Huygens Principle was proposed by the Dutch mathematician, physicist, and astronomer Christiaan Huygens, in 1690.
• This method is considered extremely authentic and powerful for studying various optical phenomena.
• It refers to the statement that all the points of the wavefront of the light in a vacuum or any transparent medium may be seen as the new source of wavelets that expand in diverse directions depending upon its velocity.
• A surface that is tangent to the wavelets forms a new wavefront and is called the envelope of the wavefront.
• Each point on the wavefront is a medium of new disturbances, henceforth, known as secondary wavelets. These secondary wavelets expand in all directions depending upon the velocity of the light till they move in the same direction.

Huygens wave theory explains concepts like reflection, refraction, interference and diffraction of light but fails to explain certain phenomena.

• Huygens assumed the light waves to be mechanical disturbances which are longitudinal in nature. Thus, failed to explain polarization.
• It could not explain the black body radiation, Compton effect and photoelectric effect.

Detriments of Phase Difference

Below mentioned are the factors on which the phase difference between two waves at a point will depend.

• The refractive index of the medium.
• The difference in path lengths of the two contrasting waves from their respective sources.
• Reflection in the path followed by the waves.

Generally, the shape of the wavefront depends upon the source of the wave and is usually in a cylindrical or spherical shape.

Interference and its types

The modification that is obtained in the distribution of the light energy by the superposition of two or more waves is called interference. There are two types of interference.

• Constructive Interference – It occurs when the new intensity is greater than the sum of the two individual wave intensities.
  • [ I > ( I1 + I2 ) ]
• Destructive Interference – It occurs when the new intensity is less than the sum of the two individual wave intensities.
  • [ I < ( I1 + I2 ) ]

Coherent and Incoherent Sources (h2)

• Coherent sources – Two sources that emit a monochromatic light continuously with a constant phase difference between them are called coherent sources.
• Incoherent sources – The sources which do not emit light with the constant phase difference are called incoherent sources.

Principle of Superposition

• It states that the number of waves travelling simultaneously in any medium are independent to each other.
• The net displacement of the particle will be equal to the sum of the individual displacements of all the waves.

Maxima and Minima are the points having maximum and minimum intensity. For instance, if the two waves reaching have a path difference of even multiple of λ/2, then the point will be maxima. Whereas, if the two waves reaching have a path difference of odd multiple of λ/2, then the point will be minima.

Young’s Double– slit experiment

Path difference, x = yd / D

Maxima, y = nλD/d

Here, n = 0,1,2,3,…

Minima, y = ( 2n + 1 ) λD/d

Here, n = 0, 1, 2, 3…

Diffraction and Single Slit Diffraction

The bending or spreading of waves that encounter an object in their path is called diffraction.

Single Slit Diffraction

Let a plane wavefront is an incident on a slit of width secondary wavelets coming from every part of AB and reach axial point P in the same phase forming central maxima. The intensity of the central maxima is maximum in this diffraction.

Brewster Law

µ = tan i

It is the unpolarized light which is incident at a polarizing angle (i) on an interface separating a rarer medium from a denser medium, of refractive index m.

The light reflected in the rarer medium is totally polarized. Reflected and refracted rays are perpendicular to each other. Reduction in Intensity:- Intensity of polarized light is 50% of that of the unpolarized light, i.e.,

Here, Ip = Intensity of polarized light and Iu = Intensity of unpolarized light. 

Solved Previous Years Questions

Q1. Two waves of the same intensity produce interference. It is found that the intensity is maximum at 4I, then intensity at the minimum will be?

1. 0
2. 2I
3. 3I
4. 4I

SOLUTION: I1 = I2 = I =a2

Imax = (a+a)2 + (2a)2 = 4a2 = 4I

Imin = (a-a)2 = 0

Q2. We know that the wavelength of light is normally incident on slit. The angular position of the second minimum from the central maximum is 300. Width of the slit should be?

1. 12 x 10 – 5cm
2. 18 x 10 – 5cm
3. 24 x 10 – 5cm
4. 36 x 10 – 5cm

SOLUTION: (c)

Q3. A slit 5 cm wide when irradiated by waves of wavelength 10mm results in the angular spread of the central maxima on either side of incident light by about

1. ½ radian
2. 1/3 radian
3. 3 radian
4. 1/5 radian

SOLUTION: Angular spread on either side is given by θ = λ/a = λ/5 radians

Some Important Formulas

• Lloyd’s single mirror – λ = β.2a/D
• Power of lens – P = 100/f
• Magnifying power of a simple microscope – M = 1+(D/f)
• Magnifying power of a compound microscope – M = L/f0(1+D/fe)

Where, f0 is the focal length of the objective.

Fe is the focal length of the eye

L is the length of the microscope tube.

Tips to solve questions on wave optics in JEE Main

• Do not waste time on the questions that involve a large number of steps or the questions which you do not know.
• Focus on having a clear understanding of the sign convention.
• Most of the questions are just there to test the concepts, so focus on solving through the right basic concepts.
• Try to visualize the problems because with an image in mind solving optics gets easier.
• Practice and solve the previous year questions always because most of the time questions are repeated with different numerals.
• Prepare the theory portion well, it might help in fetching marks.