Diffraction

A student derives the equation n λ = d sin θ for the production of a diffraction pattern on a screen. This derivation requires that:

Monochromatic light of wavelength 420 nm is incident normally on a plane transmission diffraction grating that has a slit separation of 3.6 μm.

What is the total number of maxima produced by the grating?

Figure 1 shows two prisms A and B of different refractive indices joined to make a block. A ray of monochromatic light is shown entering and then leaving the block.

Figure 1

Complete, on Figure 1, the path of the ray of light inside the block.

Deduce which prism, A or B, has the greater refractive index.

The block is used with a telescope to investigate stars. The block can be replaced with a diffraction grating.

Describe one non-astronomical application of a diffraction grating.

Figure 2 shows a spectrum of light. Two lines in the spectrum are labelled X and Y.

The light passes at normal incidence through a diffraction grating. The number of lines per metre for the grating is G.

The first-order diffraction angle of X is at 28.2° to the normal.

Calculate G.

A scientist wants to obtain an accurate value for the difference in wavelength between line X and line Y.

She has two options:

• option 1: to analyse the second-order spectrum from the original grating

• option 2: to analyse the first-order spectrum from a grating with 2G lines per metre.

Discuss which option she should choose.

A single narrow slit is illuminated with monochromatic light and a diffraction pattern is produced.

The slit width is increased.

What happens to the width and brightness of the central maximum of the diffraction

Monochromatic light of wavelength 5.8 × 10⁻⁷ m is incident normally on a plane transmission diffraction grating that has a slit separation of 2.5 × 10⁻⁶ m.

How many maxima are produced by the grating?

A diffraction grating is illuminated normally.

The second-order maximum for light of wavelength 650 nm occurs at the same angle as the third-order maximum for light of wavelength λ.

What is λ ?

A light-emitting diode (LED) emits light over a narrow range of wavelengths.

Two LEDs L_G and L_R are adjusted to give the same maximum light intensity. L_G emits green light and L_R emits red light.

Figure 3 shows how the light output of the LEDs varies with the wavelength λ.

Figure 3

Light from L_R is incident normally on a plane diffraction grating.

Determine N, the number of lines per metre on the grating.

Suggest one possible disadvantage of using the fifth-order maximum to determine N

Figure 4 shows part of the current−voltage characteristics for L_R and L_G.

When the linear part of the characteristic is extrapolated, the point at which it meets the horizontal axis gives the activation voltage V_A for the LED.

Determine, using Figure 4, V_A for L_R.

It can be shown that:

where h = the Planck constant.

Deduce a value for the Planck constant based on the data given about the LEDs.

Figure 5 shows a circuit with L_R connected to a resistor of resistance R.

The power supply has emf 6.10 V and negligible internal resistance. The current in L_R must not exceed 21.0 mA.

Deduce the minimum value of R.

Monochromatic light is incident normally on a diffraction grating that has

What is the wavelength of the light?

Figure 3 shows an arrangement to investigate diffraction. White light is incident on a single slit. After leaving the slit, the diffracted light passes through a green filter to reach the screen.

Describe the pattern produced on the screen.

The green filter is replaced with a red filter.

Describe the change in the pattern produced on the screen.

A diffraction grating is placed between the red filter and the screen. The diffraction grating has 500 lines per millimetre. Light is incident normally on the grating. Figure 4 shows the arrangement.

The wavelength of the red light is 650 nm.

In practice, the filter transmits red light with wavelengths in the range 600 nm to 700 nm.

Suggest how this affects the appearance of the maxima.

A diffraction grating has 500 lines per mm. When monochromatic light is incident normally on the grating the third-order spectral line is formed at an angle of 60° from the normal to the grating.

What is the wavelength of the monochromatic light?

One slit is then covered with opaque black paper.

What is the effect of covering one slit on the resulting interference pattern?

What is the number of lines per mm on the diffraction grating?