The document contains solutions to 15 physics problems related to optics. Some of the key details summarized are: - Problem 1 calculates the order of interference of a dark band observed when light reflects off a soap film of a given thickness and refractive index. - Problem 2 calculates the angle of a glass wedge based on fringe spacing and light wavelength. - Problem 3 calculates light wavelength using the diameter of a dark ring formed in a Newton's ring experiment. - Problem 4 calculates the refractive index of a liquid using the diameter of a bright ring.

1. Q1 A soap film of refractive index and of thickness is illuminated by white
light incident at an angle of .The light reflected by it is examined by a spectroscope in
which is found a dark band corresponding to a wavelength of . Calculate the
order of interference of the dark band.
Sol.
Or,
Hence the order,
Q2 Fringes of equal thickness are observed in a thin glass wedge of refractive index .The
fringes spacing is and wavelength of light is . Calculate the angle of wedge
in second of an arc.
Sol2.
Or,
radian
seconds of an arc
seconds of an arc

2. Q3. In a Newton’s ring arrangement, if a plano-convex lens of radius is placed on an
optically flat glass plate and is illuminated by monochromatic light .The diameter of the
dark ring in the transmitted system is Calculate the wavelrngth of light used.
Sol3. For the transmitted system
Or
Q4. Newton’s rings are formed by reflected light of wavelength with a liquid between
th
the plane and curved surfaces. If the diameter of 5 bright ring is 3mm and the radius of
curvature of the curved surface is 100 cm. Calculate the refractive index of the liquid.
Sol. Here for the nth bright ring,
Q5 In Fraunhofer diffraction due to a narrow slit a screen is placed 2m away from the lens to
obtain the pattern .If the slit width is 0.2mm and the first minima lie 5mm on either side of
the central maxima, find the wavelength of light.
Sol.
So =

3. cm
Q6 Deduce the missing order of the double slit Fraunhofer diffraction pattern if the slit width
are 0.16mm and they are 0.8mm apart.
Sol6. The direction of interference maxima are given by the eq.
The direction of diffraction minima are given by
For etc.
etc.
Thus the order 6, 12,18etc. of the interference maxima will be missing in the diffraction pattern.
Q7. What is the highest order spectrum, which may be seen with monochromatic light of
wavelength by means of a diffraction grating with 5000 lines/cm.
Sol7. Here
The maximum possible value of
Here cm

4. So,
The highest order of spectrum that can be seen is 3.
Q8. In a plane transmission grating the angle of diffraction for the second order principal
maxima for wavelength cm is . Calculate the number of lines in one cm of
the grating surface.
Sol8.
cm
Number of lines per cm=N’
Q.9 What should be the minimum number of lines in a grating which will just resolve in the
second order the lines whose wavelength are and .
Sol9. Resolving power
Approximately.
Q10.Calculate the minimum number of lines per cm in a 2.5 cm wide grating which will just
resolve the sodium lines ( and in the second order spectrum.
Sol10. Let the total number of lines required on the grating be N.

5. Number of lines per cm
Q11. If the plane of vibration of the incident beam makes an angle of with the optic axis,
compare the intensities of ordinary and extraordinary light.
Sol11. Intensities of extraordinary ray
Intensities of ordinary ray
Q13. The angle of incidence of a light beam in air onto a reflecting surface is continuously
variable. The reflected ray is found to be completely polarized when the angle of incidence
is48.0°. (a) What is the index of refraction of the reflecting material? (b) If some of the
incident light (at an angle of 48°) passes into the material below the surface, what is the
angle of refraction?
Sol13.
(a) From Brewster’s law, the index of refraction is

6. (b) From Snell’s law,
When
Note that when , as it should.
Q15. A glass wedge of angle 0.01 radian is illuminated by monochromatic light of
falling normally on it. At what distance from the edge of the wedge, will be 10 th fringes be
observed by reflected light.
Sol15
But
So
Or
=
= cm.