What will be the angular width of central maxima in Fraunhofer diffraction when the light of wavelength \(6000~\mathring A\) is used and slit width is $12\times {10}^{-5}\mathrm{cm}$?

1. 2 rad

2. 3 rad

3. 1 rad

4. 8 rad

A diffraction pattern is observed using a beam of red light. What will happen if the red light is replaced by the blue light?

A parallel beam of monochromatic light of wavelength 5000 Å is incident normally on a single narrow slit of width 0.001 mm. The light is focused by a convex lens on a screen placed on the focal plane. The first minimum will be formed for the angle of diffraction equal to:

1. 0^o

2. 15^o

3. 30^o

4. 60^o

If we observe the single slit Fraunhofer diffraction with wavelength $\mathrm{\lambda }$ and slit width d, the width of the central maxima is 2$\mathrm{\theta }$. On decreasing the slit width for the same wavelength $\mathrm{\lambda }$:

The first diffraction minima due to a single slit diffraction is at $\mathrm{\theta } = 30°$for a light of wavelength  \(5000~\mathring A.\)  The width of the slit is:

1. 5 x 10^-5 cm

2. 10 x 10^-5 cm

3. 2.5 x 10^-5 cm

4. 1.25 x 10^-5 cm

Red light is generally used to observe diffraction patterns from a single slit. If the blue light is used instead of red light, then the diffraction pattern:

The direction of the first secondary maximum in the Fraunhofer diffraction pattern at a single slit is given by:
(a is the width of the slit) 

1. $a\sin \theta =\frac{\lambda }{2}$

2. $a\cos \theta =\frac{3\lambda }{2}$

3. $a\sin \theta =\lambda$

4. $a\sin \theta =\frac{3\lambda }{2}$

In a diffraction pattern due to a single slit of width \(a\), the first minimum is observed at an angle of \(30^{\circ}\) when the light of wavelength \(5000~\mathring{\text{A}}\) is incident on the slit. The first secondary maximum is observed at an angle of:
1. \(\text{sin}^{-1}\frac{2}{3}\)
2. \(\text{sin}^{-1}\frac{1}{2}\)
3. \(\text{sin}^{-1}\frac{3}{4}\)
4. \(\text{sin}^{-1}\frac{1}{4}\)

At the first minimum adjacent to the central maximum of a single slit diffraction pattern, the phase difference between the Huygen’s wavelet from the edge of the slit and the wavelet from the midpoint of the slit is:

1. \(\frac{\pi}{4}~radian\)

2. \(\frac{\pi}{2}~radian\)

3. \(\pi~radian\)

4. \(\frac{\pi}{8}~radian\)$$

A linear aperture whose width is 0.02 cm is placed immediately in front of a lens of focal length 60 cm. The aperture is illuminated normally by a parallel beam of wavelength 5 x 10^-5 cm. The distance of the first dark band of the diffraction pattern from the center of the screen is:

1.  0.10 cm

2.  0.25 cm

3.  0.20 cm

4.  0.15 cm