A two-slit pattern is viewed on a screen 1.26 m from the slits. If the two fourth-order maxima are 53.6 cm apart, what is the total width of the central bright fringe?

= 6.55cm

Explanation:

Given that,

distance = 1.26 m

distance between two fourth-order maxima = 53.6 cm

distance between central bright fringe and fourth order maxima

y = Y / 2

= 53.6cm / 2

= 26.8 cm

=0.268 m

tan θ = y / d

= 0.268 m / 1.26 m

= 0.2127

θ = 12°

4th maxima

d sinθ = 4λ

d / λ = 4 / sinθ

d / λ = 4 / sin 12°

d / λ = 19.239

for first (minimum)

d sinθ = λ / 2

sinθ = λ / 2d

= 1 / 2 (19.239)

= 1 / 38.478

= 0.02599

θ = 1.489°

tan θ = y / d

y = d tan θ

= 1.26 tan 1.489°

= 0.03275

the total width of the central bright fringe

Y = 2y

= 2 (0.03275)

= 0.0655m

= 6.55cm