Advertisements
Advertisements
Question
For a single slit of width "a", the first minimum of the interference pattern of a monochromatic light of wavelength λ occurs at an angle of λa. At the same angle of λa, we get a maximum for two narrow slits separated by a distance "a". Explain.
Advertisements
Solution
The path difference between two secondary wavelets is given by nλ = asinθ. Since, θ is very small sinθ = θ. So, for the first order diffraction n = 1, the angle is λ/a. Now we know that θ must be very small θ = 0 (nearly) because of which the diffraction pattern is minimum.
Now for interference case, for two interfering waves of intensity I1 and I2 we must have two slits separated by a distance. We have the resultant intensity
`I=I_1+I_2+2sqrt(I_1I_2)costheta`
Since, θ = 0 (nearly) corresponding to angle λ/a so cosθ = 1 (nearly)
So,
`I=I_1+I_2+2sqrt(I_1I_2)costheta`
`=>I=I_1+I_2+2sqrt(I_1I_2)cos(0)`
`=>I=I_1+I_2+2sqrt(I_1I_2)`
We see the resultant intensity is sum of the two intensities, so there is a maxima corresponding to the angle λ/a.
This is why, at the same angle of `lambda/a`we get a maximum for two narrow slits separated by a distance "a".
APPEARS IN
RELATED QUESTIONS
Show graphically the intensity distribution in Fraunhofer's single slit diffraction experiment. Label the axes.
Draw the intensity distribution for the diffraction bands produced due to single slit ?
Two wavelengths of sodium light 590 nm and 596 nm are used, in turn to study the diffraction taking place at a single slit of aperture 2 × 10−4m. The distance between the slit and the screen is 1.5 m. Calculate the separation between the positions of the first maxima of the diffraction pattern obtained in the two cases.
Monochromatic light of wavelength 4300 Å falls on a slit of width ‘a’. For what value of ‘a’ the first maximum falls at 30° ?
In Fraunhofer diffraction, what kind of a source of light is used and where is it situated?
In a single slit diffraction experiment, how does the angular width of the central maxima change when:
- screen is moved away from the plane of the slit?
- width of the slit is increased?
- light of larger wavelength is used?
What should be the order of obstacle or aperture for diffraction of light?
A polariod (I) is placed in front of a monochromatic source. Another polatiod (II) is placed in front of this polaroid (I) and rotated till no light passes. A third polaroid (III) is now placed in between (I) and (II). In this case, will light emerge from (II). Explain.
Derive the expression for the angular position of (i) bright and (ii) dark fringes produced in a single slit diffraction.
In a single slit Fraunhofer diffraction experiment, how does the angular width of the central maximum change when the slit width is Increased?
