Question:

A light wave traveling in air undergoes diffraction as it passes through a double slit apparatus. The double slit has a separation of $d = 0.02$ mm, and the distance between the screen and the double slit is $D = 1.5$ m. The light source emits monochromatic light of wavelength $\lambda = 600$ nm.

a) Determine the separation between the first order bright fringe and the central bright fringe on the screen.

b) Calculate the angular position of the third-order bright fringe on the screen.

c) If the distance between the screen and the double slit is doubled, what changes, if any, occur in the diffraction pattern observed on the screen? Provide a brief explanation for your answer.

Answer:

a) The separation between adjacent bright fringes in the pattern formed by a double slit can be determined using the equation:

where $\Delta y$ is the separation between adjacent fringes, $\lambda$ is the wavelength of light, $D$ is the distance between the double slit and the screen, and $d$ is the slit separation.

Plugging in the given values:

Simplifying the expression, we find:

Therefore, the separation between the first order bright fringe and the central bright fringe on the screen is 45 mm.

b) The angular position $\theta$ of the bright fringes can be found using the following equation:

where $\Delta y$ is the separation between fringes and $D$ is the distance between the double slit and the screen.

Plugging in the given values:

Using a calculator, we find:

Therefore, the angular position of the third-order bright fringe on the screen is approximately $0.030$ rad.

c) If the distance between the screen and the double slit is doubled, the diffraction pattern observed on the screen will not change. This is because the pattern depends only on the ratio $\frac{D}{d}$ and not the individual values of $D$ and $d$.