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Optics Problem Sheet

The document contains 9 problems related to optics and diffraction. Problem 1 asks to calculate the intensity ratio for a two-source interference pattern. Problem 2 asks to calculate the fringe width for a two-source interference pattern. Problem 3 asks to calculate the spacing between diffraction maxima and minima for a single slit diffraction pattern observed using a converging lens.

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Rashbihari Mondal
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82 views1 page

Optics Problem Sheet

The document contains 9 problems related to optics and diffraction. Problem 1 asks to calculate the intensity ratio for a two-source interference pattern. Problem 2 asks to calculate the fringe width for a two-source interference pattern. Problem 3 asks to calculate the spacing between diffraction maxima and minima for a single slit diffraction pattern observed using a converging lens.

Uploaded by

Rashbihari Mondal
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Problem set Optics

1. Find the ratio of the intensity at point P to that at a maximum when the path difference S1P
- S2P = λ/6. (S1 and S2 are the source position).

2. Two point source separated by a distance of 0.5 mm produced an interference pattern on a


screen placed at a distance of 50 cm from the sources. Calculate the fringe width for λ = 5 ×
10–5 cm.

3. A parallel beam of light is incident normally on a narrow slit of width 0.2 mm. The
Fraunhofer diffraction pattern is observed on a screen which is placed at the focal plane of a
convex lens whose focal length is 20 cm. Calculate the distance between the first two minima
and the first two maxima on the screen. Assume that λ = 5 × 10–5 cm, angle of diffraction is
very small and that the lens is placed very close to the slit.

4. Consider a parallel beam of light (λ = 5 × 10–5 cm) to be incident normally on a long


narrow slit of width 0.2 mm. A screen is placed at a distance of 3 m from the slit. Assuming
that the screen is so far away that the diffraction is essentially of the Fraunhofer type.
Calculate the total width of the central maximum.

5. A plane wave (λ = 5000 Å) falls normally on a long narrow slit of width 0.5 mm. Calculate
the angles of diffraction corresponding to the first three minima.

6. Consider a set of two slits each of width b = 5 × 10–2 cm and separated by a distance d =
0.1 cm, illuminated by a monochromatic light of wavelength 6.328 × 10–5 cm. If a convex
lens of focal length 10 cm is placed beyond the double-slit arrangement, calculate the
positions of the minima inside the first diffraction minimum.

7. Consider a diffraction grating of width 5 cm with slits of width 0.0001 cm separated by a


distance of 0.0002 cm. What is the corresponding grating element? How many orders would
be observable at λ = 5.5 × 10–5 cm? Calculate the width of the principal maximum. Would
there be any missing orders? What will be the resolving power in each order?

8. A grating (with 15,000 lines per inch) is illuminated by sodium light. The grating spectrum
is observed on the focal plane of a convex lens of focal length 10 cm. Calculate the separation
between the D1 and D2 lines of sodium. (The wavelengths of the D1 and D2 lines are 5890
and 5896 Å, respectively.)

9. Consider a diffraction grating with 15,000 lines per inch. Show that if we use a white light
source, the second and third order spectra overlap. (Consider red (λ = 7 × 10–5 cm) and violet
(λ = 4 × 10–5 cm) for the calculation.)

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