Tutorial Sheet Diffraction
1
DEPARTMENT OF PHYSICS BBDNIIT B. TECH. FIRST SEMESTER 2014-2015 UNIT III: WAVE OPTICS (DIFRACTION) Q.1 What is meant by diffraction of light? Distinguish between Fresnels and Fraunhofer classes of diffraction. Q.2 Discuss Fraunhofer diffraction due to single slit Derive an expression for intensity distribution and show that the intensities of the successive maximum are nearly 1:4/9π 2 :4/25 π 2 :4/49π 2 . Q.3 A single slit is illuminated by light composed of two wavelengths λ 1 and λ 2 .One observes that due to fraunhofer diffraction the first minima obtained for λ 1 coincides with second diffraction minima of λ 2 .What is the relation between λ 1 and λ 2. Q.4 In Fraunhofer diffraction due to a single slit, the screen is placed 2m away from the slit. If the slit width is 0.2 mm and the first minima lies 5mm on either side of the central maxima, find the wavelength of incident light. Q.5 Calculate the angle at which the first dark band and the next bright band are formed in the Fraunhofer diffraction pattern of a slit of 0.3 mm width with monochromatic light of wavelength 6000Å. Q.6 A lens whose focal length is 50 cm. forms a Fraunhofer diffraction of a single slit of 0.3 mm. width. Calculate the distances of the first dark band and of the next bright band on either side of the central maximum. The wavelength of light used is 5890Å. Q.7 What do you understand by dispersive power of a plane transmission grating? Derive the expression for it. Q.8 What do you understand by missing order spectrum? Show that only first order is possible if the width of a grating element is less than twice the wavelength of light. Q.9 Show that the angular half width of a principal maximum in a plane transmission grating does not depend upon the number of lines per unit length, but it depends on the total number of lines present on the grating. Q.10 A diffraction grating used at normal incidence gives a yellow l ine (λ =6000Ǻ) in a certain special order superimposed on a blue line (λ =4800Ǻ) of the next higher order. If the angle of diffraction is sin -1 (3/4), calculate the grating element. Q.11 How many orders will be visible, if the wavelength of the incident radiation is 5000 Ǻ and the number of lines on the grating is 2620 per inch. Q.12 In a grating spectrum, which spectral line in 5 th order will overlap with 4 th order line of 5890Å? Q.13 What is meant by the resolving power of an optical instrument? Explain Rayleigh’s criter ion for just resolution. Define limit of resolution and resolving power. Q.14 What do you understand by resolving power of a grating? Derive the necessary expression for it. Q.15 Calculate the minimum number of lines in a grating which will just resolve the lines of wavelengths 5890Å and 5896Å in the second order. Q.16 A grating has 6,000 lines per cm drawn on it. If its width is 10 cm, calculate A. The resolving power in the second order. B. The smallest wavelength that can be resolved in the third order in 6000Å wavelength region.
description
diffraction
Transcript of Tutorial Sheet Diffraction
DEPARTMENT OF PHYSICS BBDNIIT B. TECH. FIRST SEMESTER 2014-2015
UNIT III: WAVE OPTICS (DIFRACTION)
Q.1 What is meant by diffraction of light? Distinguish between Fresnels and Fraunhofer classes of
diffraction.
Q.2 Discuss Fraunhofer diffraction due to single slit Derive an expression for intensity distribution and
show that the intensities of the successive maximum are nearly 1:4/9π2:4/25 π
2:4/49π
2.
Q.3 A single slit is illuminated by light composed of two wavelengths λ1 and λ2.One observes that due
to fraunhofer diffraction the first minima obtained for λ1 coincides with second diffraction minima
of λ2.What is the relation between λ1 and λ2.
Q.4 In Fraunhofer diffraction due to a single slit, the screen is placed 2m away from the slit. If the slit
width is 0.2 mm and the first minima lies 5mm on either side of the central maxima, find the
wavelength of incident light.
Q.5 Calculate the angle at which the first dark band and the next bright band are formed in the
Fraunhofer diffraction pattern of a slit of 0.3 mm width with monochromatic light of wavelength
6000Å.
Q.6 A lens whose focal length is 50 cm. forms a Fraunhofer diffraction of a single slit of 0.3 mm.
width. Calculate the distances of the first dark band and of the next bright band on either side of the
central maximum. The wavelength of light used is 5890Å.
Q.7 What do you understand by dispersive power of a plane transmission grating? Derive the
expression for it.
Q.8 What do you understand by missing order spectrum? Show that only first order is possible if the
width of a grating element is less than twice the wavelength of light.
Q.9 Show that the angular half width of a principal maximum in a plane transmission grating does not
depend upon the number of lines per unit length, but it depends on the total number of lines present
on the grating.
Q.10 A diffraction grating used at normal incidence gives a yellow line (λ =6000Ǻ) in a certain special
order superimposed on a blue line (λ =4800Ǻ) of the next higher order. If the angle of diffraction is
sin-1
(3/4), calculate the grating element.
Q.11 How many orders will be visible, if the wavelength of the incident radiation is 5000 Ǻ and the
number of lines on the grating is 2620 per inch.
Q.12 In a grating spectrum, which spectral line in 5th
order will overlap with 4th
order line of 5890Å?
Q.13 What is meant by the resolving power of an optical instrument? Explain Rayleigh’s criterion for
just resolution. Define limit of resolution and resolving power.
Q.14 What do you understand by resolving power of a grating? Derive the necessary expression for it.
Q.15 Calculate the minimum number of lines in a grating which will just resolve the lines of
wavelengths 5890Å and 5896Å in the second order.
Q.16 A grating has 6,000 lines per cm drawn on it. If its width is 10 cm, calculate
A. The resolving power in the second order.
B. The smallest wavelength that can be resolved in the third order in 6000Å wavelength region.
