Question

A metallic sheet has a large number of slits, 5.0 mm wide and 20 cm apart, and is used as a diffraction grating for microwaves. A wide parallel beam of microwaves is incident normally on the grating. In the situation above, the microwave wavelength is 6.0 cm. The largest angle from the normal, at which an intensity maximum occurs, is closest to: Situation A metallic sheet has a large number of slits, 5.0 mm wide and 20 cm apart, and is used as a diffraction grating for microwaves. A wide parallel beam of microwaves is incident normally on the grating. In the situation above, the microwave wavelength is 6.0 cm. The largest angle from the normal, at which an intensity maximum occurs, is closest to: 79° 64° 84° 69° 74°

Answer 1

Slit width, a= 5.0mm=0.5cm

Distance between slits, b= 20cm

Wavelength, $\lambda= 6cm$

n= order of diffraction

Then using diffraction equation,

   $(a+b)sin\theta= n\lambda$

or $((0.5+20)\times 10^{-2})sin\theta= n(6 \times 10^{-2})$

   $n= \frac{20.5sin\theta}{6}= 3.41 sin\theta$

Now for angle= 79^o, order of diffraction will be

   $n_1= 3.41 sin79^\circ= 3.34$ , Can't possible since "n" has to be an integer.

Now for angle= 64^o, order of diffraction will be

   $n_2= 3.41 sin64^\circ= 3.06\sim 3$ , Can be possible since "n" has to be an integer.

Now for angle= 84^o, order of diffraction will be

   $n_3= 3.41 sin84^\circ= 3.39$ , Can't possible since "n" has to be an integer.

Now for angle= 69^o, order of diffraction will be

   $n_4= 3.41 sin69^\circ= 3.18$ , Can't possible since "n" has to be an integer.

Now for angle= 74^o, order of diffraction will be

   $n_5= 3.41 sin74^\circ= 3.27$ , Can't possible since "n" has to be an integer.

Hence correct option: Maximum angle is closest to 64^o.