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

Consider the equation $d\sin \theta =n\lambda$. State and explain how the interference pattern would change when:

(b) The grating is changed for one with more lines per $\mathrm{cm}$ for the same incident light.

A student is trying to make an accurate measurement of the wavelength of green light from a mercury lamp. The wavelength $\lambda$ of this light is $546 \mathrm{nm}$. Using a double-slit of separation $0.50 \mathrm{mm}$, the student can see $10$ clear bright fringes on a screen at a distance of $0.80 \mathrm{m}$ from the slits. The student can measure their overall width to within $\pm 1 \mathrm{mm}$

Using a ruler. The student then tries an alternative experiment using a diffraction grating with $3000$ lines ${\mathrm{cm}}^{-1}$. The angle between the two second-order maxima can be measured to within $\pm 0.1°$.

(a) Determine the width of the $10$ fringes that the student can measure in the first experiment.

A student is trying to make an accurate measurement of the wavelength of green light from a mercury lamp. The wavelength $\lambda$ of this light is $546 \mathrm{nm}$. Using a double-slit of separation $0.50 \mathrm{mm}$, the student can see $10$ clear bright fringes on a screen at a distance of $0.80 \mathrm{m}$ from the slits. The student can measure their overall width to within $\pm 1 \mathrm{mm}$

Using a ruler. The student then tries an alternative experiment using a diffraction grating with $3000$ lines ${\mathrm{cm}}^{-1}$. The angle between the two second-order maxima can be measured to within $\pm 0.1°$.

(b) Determine the angle of the second-order maximum that the student can measure in the second experiment.

A student is trying to make an accurate measurement of the wavelength of green light from a mercury lamp. The wavelength $\lambda$ of this light is $546 \mathrm{nm}$. Using a double-slit of separation $0.50 \mathrm{mm}$, the student can see $10$ clear bright fringes on a screen at a distance of $0.80 \mathrm{m}$ from the slits. The student can measure their overall width to within $\pm 1 \mathrm{mm}$

Using a ruler. The student then tries an alternative experiment using a diffraction grating with $3000$ lines ${\mathrm{cm}}^{-1}$. The angle between the two second-order maxima can be measured to within $\pm 0.1°$.

(c) Based on your answers to parts $\mathrm{a}$ and $\mathrm{b}$, suggest which experiment you think will give the more accurate value of $\lambda$.

White light is incident normally on a diffraction grating with a slit-separation $d$ of $2.00\times {10}^{-6} \mathrm{m}$. The visible spectrum has wavelengths between $400 \mathrm{nm}$ and $700 \mathrm{nm}$.

(a) Calculate the angle between the red and violet ends of the first-order spectrum.

White light is incident normally on a diffraction grating with a slit-separation $d$ of $2.00\times {10}^{-6} \mathrm{m}$. The visible spectrum has wavelengths between $400 \mathrm{nm}$ and $700 \mathrm{nm}$.

(b) Explain why the second-and third-order spectra overlap.