Use the equation $\lambda =\frac{ax}{D}$ to explain the following observations:

(a) With the slits closer together, the fringes are further apart.

Use the equation $\lambda =\frac{ax}{D}$ to explain the following observations:

(b) Interference fringes for blue light are closer together than for red light.

Use the equation $\lambda =\frac{ax}{D}$ to explain the following observations:

(c) In an experiment to measure the wavelength of light, it is desirable to have the screen as far from the slits as possible.

Monochromatic light is incident normally on a diffraction grating having $3000$lines per centimetre. The angular separation of the zeroth- and first-order maxima is found to be $10°$. If $\lambda =580 \mathrm{nm}$, calculate the angle $\theta$ for the second-order maximum.

Monochromatic light is incident normally on a diffraction grating having $3000$lines per centimetre. The angular separation of the zeroth- and first-order maxima is found to be $10°$. If $\lambda =580 \mathrm{nm}$, calculate the angle $\theta$ for the second-order maximum.

(b) Repeat the calculation of $\theta$ for $n=3,4$, and so on. Determine how many maxima can be seen. Explain your answer.

Consider the equation $\mathrm{dsin\theta }=\mathrm{n\lambda }$. State and explain how the interference pattern would change when:

(a) The wavelength of the incident light is increased for the same grating