PHYS1241 Tutorial Problems Week 10

1. A diffraction grating has a resolving power of R = /Δ = Nm. Calculate the corresponding

frequency range, Δ , that can just be resolved.

[ Ans: Δ = c/(Nm ) ]

2. Why do sunglasses made of polarizing materials have a marked advantage over those that only

depend on the absorption effects?

3. What must be the angle between the polarization axes of two ideal polarizing sheets, if the

transmitted light intensity is to be 25% of the intensity of unpolarised light incident on the first

sheet?

[Ans: 450 ]

4. An unpolarised beam of light is incident on a group of 4 polarising sheets which are lined up so

that the vibration direction of each is rotated by 300 clockwise with respect to the preceding sheet.

What fraction of the incident light is transmitted?

[Ans: 21% ]

5. Lighting produces a maximum air temperature on the order of 104 K, whereas a nuclear explosion

produces a temperature on the order of 107 K. (a) Use Wien’s displacement law to find the order

of magnitude of the wavelength of the thermally produced photons radiated with greatest intensity

by of these sources. (b) Name the part of the E.M. spectrum where you would expect each to

radiate most strongly.

[Ans: (a) lightning 10-7

m, nuclear exp: 10-10

m; (b) U.V., X-ray]

6. The average threshold of dark adapted vision for humans is 4 x 10-11

W/m2 at a central wavelength

of 500nm. If light with this intensity and wavelength enters the eye and the pupil is open to its

maximum diameter of 8.5 mm, how many photons per second enter the eye?

[Ans: 5.71 x 103 photons per second]

7. In the photoelectric effect, why does the existence of a cut-off frequency speak in favour of the

photon theory and against the wave theory?

8. List the assumptions made by Planck in connection with the cavity radiation problem, by Einstein

in connection with the photoelectric effect, and by Compton in connection with the Compton

effect.

9. Sketch the experimental arrangement needed to measure the photoelectric effect.

10. Show that the energy E of a photo in eV is related to its wavelength, , in nm by: E = 1240/

11. Incident photons strike a sodium surface having a work function of 2.2 eV, causing photoelectric

emission. When a stopping potential V = 5.0 V is imposed, there is no photocurrent. Calculate

the wavelength of the incident photons. [Ans: 172 nm]