Advertisements
Advertisements
Question
Using the monochromatic light of the wavelength in the experimental set-up of the diffraction pattern as well as in the interference pattern where the slit separation is 1 mm, 10 interference fringes are found to be within the central maximum of the diffraction pattern. Determine the width of the single slit, if the screen is kept at the same distance from the slit in the two cases.
Advertisements
Solution
If a is the width of the single slit, then for the central maximum of the single slit diffraction pattern,
`sin theta ≈ theta = lambda_1/"a"`
⇒ Total angular width, `2 theta = (2lambda_1)/"a"` ...(1)
For 10 interference fringes of the double-slit interference pattern to lie within the central maximum of the single slit pattern,
⇒ Total angular width, `2 theta = 10(2lambda_2)/"d"` ...(2).....(d is the separation between the slits).
From equation 1 and 2, `(2lambda_1)/"a" = (102lambda_2)/"d"`
As the light of the same wavelength is used in both cases, so λ1 = λ2
Hence,
`2/"a" = 10/"d"`
⇒ `"a" ="d"/5 = 1/5 "mm" = 0.2 "mm"`
⇒ a = 0.2 mm
APPEARS IN
RELATED QUESTIONS
'Two independent monochromatic sources of light cannot produce a sustained interference pattern'. Give reason.
Two monochromatic rays of light are incident normally on the face AB of an isosceles right-angled prism ABC. The refractive indices of the glass prism for the two rays '1' and '2' are respectively 1.35 and 1.45. Trace the path of these rays after entering the prism.
If a monochromatic source of light is replaced by white light, what change would you observe in the diffraction pattern?
The following figure shows three equidistant slits being illuminated by a monochromatic parallel beam of light. Let \[B P_0 - A P_0 = \lambda/3\text{ and }D > > \lambda.\] (a) Show that in this case \[d = \sqrt{2\lambda D/3}.\] (b) Show that the intensity at P0 is three times the intensity due to any of the three slits individually.
"Monochromatic light should be used to produce pure spectrum". Comment on this statement.
State with reason, how the linear width of the central maximum will be affected if
(i) monochromatic yellow light is replaced with red light, and
(ii) distance between the slit and the screen is increased.
Monochromatic light of wavelength 650 nm falls normally on a slit of width 1 : 3 × 10-4 cm and the resulting Fraunhofer diffraction is obtained on a screen. Find the angular width of the central maxima.
Answer the following question.
In the diffraction due to a single slit experiment, the aperture of the slit is 3 mm. If monochromatic light of wavelength 620 nm is incident normally on the slit, calculate the separation between the first order minima and the 3rd order maxima on one side of the screen. The distance between the slit and the screen is 1.5 m.
Monochromatic light of wavelength 396 nm is incident on the surface of a metal whose work function is 1.125 eV. Calculate:
- the energy of an incident photon in eV.
- the maximum kinetic energy of photoelectrons in eV.
The Figure below shows a ray of monochromatic light LM incident on the first surface AB of a regular (equilateral) glass prism ABC. The emergent ray grazes the adjacent surface AC. Calculate the angle of incidence. (Refractive Index of glass = 1.5)
