A screen is placed 1.60 m behind a single slit. The central maximum in the resulting diffraction pattern on the screen is 1.40 cm wide-that is, the two first-order diffraction minima are separated by 1.40 cm. What is the distance between the two second-order minima?

distance between the two second-order minima is 2.8 cm

Explanation:

Given data

distance = 1.60 m

central maximum = 1.40 cm

first-order diffraction minima = 1.40 cm

to find out

distance between the two second-order minima

solution

we know that fringe width = first-order diffraction minima / 2

fringe width = 1.40 / 2 = 0.7 cm

and

we know fringe width of first order we calculate slit d

β1 = m1λD/d

d = m1λD/β1

and

fringe width of second order

β2 = m2λD/d

β2 = m2λD / (m1λD/β1)

β2 = (m2 / m1) β1

we know the two first-order diffraction minima are separated by 1.40 cm

so

y = 2β2 = 2 (m2 / m1) β1

put here value

y = 2 (2 / 1) 0.7

y = 2.8 cm

so distance between the two second-order minima is 2.8 cm