Question

Light of frequency 500 THz is incident on a single slit and forms a
diffraction pattern. The first diffraction minimum forms at an angle of 2.4
x 10 rad to the central maximum. The frequency of the light is now changed to
750 THz. What is the angle between the first diffraction minimum and the central
maximum?
A. 1.6 × 10 rad
B. 1.8 × 10 rad
C. 2.4 × 10 rad
D. 3.6 × 10 rad
Please put the proccess of the answer and an explanation of it.

Answer 1

The angle between the first diffraction minimum  is  $1.8 *10^-^1$ rad,

The angle θ of the first diffraction minimum in a single-slit diffraction;

sin(θ) = (mλ) / b

m = order of the minimum (m = 1 for the first minimum)

λ = wavelength of the light,

b = width of the slit.

For the given frequency of 500 THz,

λ = c / f

c = speed of light in vacuum

f = frequency.

λ = c / f

= $(3.0 *10^8 m/s) / (500 *10^1^2 Hz)$

= $6.0 *10^-^7 m$

nOW,

b = (mλ) / sin(θ)

= $1 *6.0 *10^-^7 / sin(2.4 *10^-3 rad)$

= $2.5 *10^-^5$m

Now, for the new frequency of 750 THz

λ' = c / f'

= $3.0 *10^8 / 750 *10^1^2$

= $4.0 *10^-^7 m$

sin(θ') = (mλ') / b

= $1 *4.0 * 10^-^7 m/ 2.5 *10^-^5 m$

= $1.6 *10^-^2$

θ' = $sin^-^1(1.6 * 10^-^2)$

= $1.8 *10^-^1 rad$

Hence, the angle between the first diffraction minimum and the central

maximum is $1.8 *10^-^1 rad$

To know more about angle visit

: brainly.in/question/11418559

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