The condition for obtaining secondary maxima in the diffraction pattern due to single slit is :

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : An electron microscope can achieve better resolving power than an optical microscope.

Reason R : The de Broglie's wavelength of the electrons emitted from an electron gun is much less than wavelength of visible light.

In the light of the above statements, choose the correct answer from the options given below:

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.

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.

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.

Represent the union of two sets by Venn diagram for each of the following.

$X=\{x | x$ is a prime number between $80$ and $100\}$

$Y=\{y | y$ is an odd number between $90$ and $100\}$

A grating with $400 \mathrm{lines} \mathrm{per} \mathrm{mm}$ is illuminating with the light of wavelength $600.0\mathrm{nm}$.

a. Determine the angles at which maxima are observed.

(b) This diagram shows the experimental setup (left) used to analyse the spectrum of a sodium discharge lamp with a diffraction grating with $500$ lines ${\mathrm{mm}}^{-1}$, and the spectral lines observed (right) in the developed photographic film.

(i) Explain why two spectra are observed.

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

One of the spectral lines from a hydrogen discharge lamp has wavelength $656 \mathrm{nm}$. This light is incident normally at a diffraction grating with $5000$ lines ${\mathrm{cm}}^{-1}$.

Calculate the angles for the first- and second-order maxima for this light

The spectrum of sodium includes two lines at wavelength $588.995 \mathrm{nm}$ and $589.592\mathrm{nm}$. A sodium lamp is viewed by a diffraction grating that just manages to resolve these two lines in the third order at $12°$. Determine

b. The total number of ruling on the grating.

(b) This diagram shows the experimental setup (left) used to analyse the spectrum of a sodium discharge lamp with a diffraction grating with $500$ lines ${\mathrm{mm}}^{-1}$, and the spectral lines observed (right) in the developed photographic film.

(ii) Describe two differences between these two spectra.

(b) This diagram shows the experimental setup (left) used to analyse the spectrum of a sodium discharge lamp with a diffraction grating with $500$ lines ${\mathrm{mm}}^{-1}$, and the spectral lines observed (right) in the developed photographic film.

(iii) The green maximum near end $\mathrm{A}$ is at an angle $\mathrm{\theta }$ of $19.5°$. Calculate the wavelength of the green light.

A grating with $400 \mathrm{lines} \mathrm{per} \mathrm{mm}$ is illuminating with the light of wavelength $600.0\mathrm{nm}$.

b. Determine the largest order that can be seen with which this grating and this wavelength.