**NCERT solutions for class 12 Physics chapter 10 Wave Optics:** The second part of the unit optics is wave optics. The solutions of NCERT class 12 physics chapter 10 wave optics will help in understanding the formulas and derivations that are dealt with in the chapter. Do you know that the Dutch Physicist Christiaan Huygens has put forward the wave theory of light in 1678? This is beautifully explained in NCERT book and questions based on this wave model are discussed in the CBSE NCERT solutions for class 12 physics chapter 10 wave optics. Also, one of the facts says, the wavelength of the electromagnetic wave is very small in comparison to the dimension of the mirror or lens, so light is assumed to be traveled in a straight line. NCERT solutions for class 12 physics chapter 10 wave optics have questions on the concept of diffraction and polarisation which is important for the board examination. Problems from youngs double-slit experiment and single diffraction pattern from the class 12 physics chapter 10 are also expected in the board exams. The solutions of NCERT helps in building a strong base on the topics discussed in the chapter.

Given a monochromatic light has a wavelength of .

And as we know the speed of the light in air is, .

Refractive index of water,

Therefore we have now,

The ray is incident on the medium, and then it gets reflected back to the same medium therefore, the wavelength, speed, and frequency will be the same as that of the incident ray.

We have the frequency of light is given by the relation,

**Therefore the speed, frequency, and the wavelength of the reflected light are , , and respectively.**

Given,

The wavelength of the monochromatic light

Refractive index of the water

b)In the case of refraction, speed and wavelength will change as the medium is changing however, the frequency will remain the same because it doesn't change when the medium is changed,

so, frequency

Speed of rays: speed of rays in water with refractive index 1.33 is

Now, the Wavelength of light

Hence the wavelength of light is 444.01nm, frequency is and speed is .

**Q10.2 (a) **What is the shape of the wavefront in each of the following cases:

(a) Light diverging from a point source.

The shape of wavefront when light is diverging from a point source is Spherical since light travels in all direction.

**Q10.2 (b) **What is the shape of the wavefront in each of the following cases:

(b) Light emerging out of a convex lens when a point source is placed at its focus.

The shape of light emerging out of a convex lens when a point source is placed at its focus is Parallel .when light rays come from infinity parallelly, they intersect at focus of convex lens and hence when light is emerging from the focus, the rays will get parallel to each other after coming out of the convex lens, because path of light rays are reversible.

(c) The portion of the wavefront of light from a distant star intercepted by the Earth

The portion of the wavefront of the light from the distant star which is seen from earth is plane since a small area of a large sphere will nearly look like a plane.

Given,

Refractive index of the glass = 1.5

Speed of light in vaccum

Now,

As we know,

Refractive index of a medium

where is the speed of light in that medium.

so from here,

Hence the speed of light in water is

No, the speed of light in glass is not independent of the colour. The colour of the light does influence the refractive index and speed of light in the medium. The refractive index of the violet light is greater than the refractive index of red light and hence red component of the white light travels faster in the glass than the red component of the light.

as

the more the refractive index, the lesser the speed.

Given,

Distance between screen and slit

Distance between slits

Distance between central and fourth bright fringe

Now,

as we know, the distance between two fringes in a constructive interference is given by

where order of fringe (which is 4 here) and is the wavelength of light we are using.

so from here,

Hence wavelength os the light is 600nm

**Q10.5 **In Young’s double-slit experiment using monochromatic light of wavelength , the intensity of light at a point on the screen where path difference is , is K units. What is the intensity of light at a point where path difference is ?

**Answer:**

Given, in youngs double-slit experiment.

the wavelength of monochromatic light =

The intensity of light when the path difference is = K

Now,

As we know,

The phase difference is given by

also

Total Intensity

Let

Now, when path difference is

the phase difference angle

so,

Now, when path difference is

Intensity of light

Now comparing intensity at both cases

Hence intensity will reduce to one-fourth of initial when path difference changes from to .

**Q10.6 **A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes in a Young’s double-slit experiment.

Given,

The wavelength of one light beam :

The wavelength of another Light beam

Let, the distance between the two-slit be and distance between slit and screen is

Now,

As we know, the distance of nth bright fringe from central maxima is given by

so for 3rd fringe,

Hence distance of 3rd fringe from central maxima is . Here value D and d are not given in the question.

Let the nth bright fringe due to wavelength, and (n − 1)^{th}bright fringe due to wavelength coincide on the screen. We can equate the conditions for bright fringes as:

Hence, the least distance from the central maximum can be obtained by the relation:

Hence we can find out X if D and d are given.

Given

The angular width of the fringe when the medium is air

The distance of the screen from the slit

The wavelength of light we are using

Refractive index of water

let angular width of fringe when the medium is water

Now, as we know the angular width is given by

so,

From here

Hence angular width of the fringe in the water is .

**Q10.8 **What is the Brewster angle for air to glass transition? (Refractive index of glass = 1.5.)

Given,

Refractive index of glass

Now as we know,

where is the polarizing angle, also called the Brewster angle.and is the refractive index.

so from here

Hence Brewster angle is .

Given,

Wavelength of light

Speed of light

Now,

Wavelength and frequency will be the same when the ray is reflected.

Frequency of reflected light

Hence wavelength and frequency of light is and respectively.

Now,

as per the law of reflection, angle of incidence is always equal to angle of reflection .

Now, when the reflected ray is perpendicular with incidence ray,

Hence the angle of incidence is 45 for this condition.

Given

Aperture

Wavelength of light

Now,

Distance for which ray optics is a good approximation also called Fresnel's distance:

Hence distance for which ray optics is a good approximation is 40m.

Given,

wavelength Hα line emitted by hydrogen:

star is red-shifted by

let velocity of the star be

Now,

as we know,

from here

Hence speed at which star is receding away is

According to corpuscular theory, when corpuscle of the light goes from rare medium to denser medium, the component of their velocity along the surface of the interface remains the same.

So we can write

As ,

That is light should be faster in the dense medium than in rare medium.this is the opposite of what we see experimentally.

Huygens wave theory predicts that light is faster in a rare medium which matches with our experiments observation.

Let an object M is placed in front of a plane mirror AB at a distance r .

A circle is drawn from the centre, such that it just touches the plane mirror at point P. according to the Huygens’ principle, AB is the wavefront of the incident light .

If the mirror is absent then a similar wavefront A'B' would form behind M at a distance r.

A'B' can be considered as a virtual reflected ray for the plane mirror. Hence a point object placed in front of the plane mirror produces an image at the same distance as the object.

The speed of light in a vacuum is constant and independent of anything according to Einstein's theory of relativity.

(b) the speed of light in a medium (say, glass or water), depend?

The speed of light in any medium depends upon the wavelength of the light and does not depends on the nature of the source, direction of propagation, the motion of the source and/or observer, and intensity of the wave.

The sound wave requires a medium for propagation.so, even though both given situation may relate to the same relative motion, they are not identical physically since, the motion of the observer, relative to the medium is different in two situations. Hence, we cannot expect the Doppler formula to be identical in both given cases.

When light waves are in a vacuum, there is clearly nothing to distinguish between two cases.

for light propagation in a medium, two situations are not identical for the same reason as in the case of sound waves.

Given,

Wavelength of light = 600nm

Angular fringe width

Hence spacing required between the two slits is .

**Q10.17 (a) **Answer the following questions:

As we know,

width of the central diffraction band is given by

where d is the width of the slit.

So when we double the width of the slit, the size of the central diffraction band reduces to half of its value. But, the light amplitude becomes double, which increase the intensity 4 times.

**10.17 (b)** ** **Answer the following questions:

When we have a width in the order of , the intensity of interference fringes in Young's double-slit experiment is modified by the diffraction pattern of each slit.

**Q10.17** ** (c)**** **Answer the following questions:

A bright spot is seen at the centre of the shadow of the obstacle because wave diffracted from the edge of a circular obstacle interfere constructively at the centre of the shadow producing the bright spot.

**Q10.17 (d) **Answer the following questions:

The size of obstacle should be comparable to the wavelength for diffraction of waves by obstacles, through a large scale.

This comes from

This implies

it means the light goes almost unbent and hence student are unable to see each other.

**Q10.17** **(e) **Answer the following questions:

Typical size of the obstacle is much larger than the wavelength of light. Hence the diffraction effect is negligibly small. thus the assumption that light travels in a straight line can be safely used in day to day life.

Given,

Distance between two towers = 40km

size of aperture =

Now,

As we know

Fresnel's distance is equal to half of the distance between towers

Also from the formula:

Hence this is the required longest wavelength of the radio wave, which can be sent in between the towers without considerable diffraction effect.

**Q10.19 **A parallel beam of light of wavelength 500 nm falls on a narrow slit and the resulting diffraction pattern is observed on a screen 1 m away. It is observed that the first minimum is at a distance of 2.5 mm from the centre of the screen. Find the width of the slit.

Given

The distance of the screen from the slit,

The distance of the first minimum

The wavelength of the light

Now,

As we know,

Hence, the width of the slit is 0.2 mm.

When a low flying aircraft passes overhead, we notice slight shaking in pictures of the TV. This is because aircraft interferes with signals and reflects it. So the shaking we see is the interference of direct signal and reflected signal.

The superposition principle comes from the linear character of the differential equation of wavemotion.that is if and are the solution of any wave equation, then linear combination of and is also the solution of the wave equation.

Let the width of the slit be divided into n equal parts so that

Now,

At this angle, each slit will make the first diffraction minimum. therefore the resultant intensity for all the slits will be zero at the angle of .

**Chapter list for class 12 physics is given below-**

**Subjectwise solutions-**

- In 2019 CBSE board exam 11 marks questions were asked from the unit optics which includes NCERT chapters 9 and 10 of class 12 physics.
- For competitive exams also the CBSE NCERT solutions for class 12 physics chapter 10 wave optics are important. Questions from the topic young's double-slit experiment are frequently asked in the competitive exams like NEET and JEE Main.
- NCERT solutions for class 12 physics chapter 10 wave optics are important to score well in exams.

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