Question

Light of wavelength 600 nm passes though two slits separated by 0.22mm and is observed on a screen 1.1m behind the slits. The location of the central maximum is marked on the screen and labeled y = 0.
A) At what distance, on either side of y = 0, are the m = 1 bright fringes ?

B) A very thin piece of glass is then placed in one slit. Because light travels slower in glass than in air, the wave passing through the glass is delayed by 5.0

Answer 1

Complete Part B:

B) A very thin piece of glass is then placed in one slit. Because light travels slower in glass than in air, the wave passing through the glass is delayed by 5.0 * 10⁻¹⁶ s in comparison to the wave going through the other slit. What fraction of the period of the light wave is this delay?

Answer:

A) y = 3.0 mm

B) Fraction of delay = 0.25

Explanation:

wavelength of the light, $\lambda = 600 nm = 600 * 10^{-9} m$

Separation between the two slits, d = 0.22 mm = 0.00022 m

Distance between the screen and the slit, L = 1.1 m

The distance of the bright fringes, $y = \frac{m \lambda L}{d}$

$y = \frac{1 * 600 * 10^{-9}* 1.1 }{0.00022}$

$y = 0.003 m$

$y = 3.0 mm$

b) The period of the light wave in air  can be calculated by using the formula

$c = \frac{\lambda}{T} \\T = \frac{\lambda}{c}$

c = 3 * 10⁸ m/s

$T = \frac{600 * 10^{-9} }{3 * 10^{8} }$

$T = 2 * 10^{-15} sec$

The time delay due to the slow travel of light in glass, $\triangle t = 5 * 10^{-16} s$

Fraction of delay = $\frac{5 * 10^{-16} }{2 * 10^{-15} }$

Fraction of delay = 0.25

Answer 2

Answer:

$y(m=1)=\frac{(1)(600*10^{-9}m)(1.1m)}{0.22m}=3*10^{-6}m\\\\y(m=1)=\frac{(-1)(600*10^{-9}m)(1.1m)}{0.22m}=-3*10^{-6}m$

Explanation:

We have to take into account the expression for the position of the fringes

$dsen\theta=m\lambda\\y=\frac{m\lambda D}{d}$

where m is the number of the maximum, d is the separation of the slits, D is the distance to the screen.

(a) By replacing we obtain

$y(m=1)=\frac{(1)(600*10^{-9}m)(1.1m)}{0.22m}=3*10^{-6}m\\\\y(m=1)=\frac{(-1)(600*10^{-9}m)(1.1m)}{0.22m}=-3*10^{-6}m$

(b)  more information is required to solve this point. Please complete the information.

HOPE THIS HELPS!