K A Tsokos Solutions for Chapter: Wave Phenomena (HL), Exercise 4: Test yourself

The Arecibo radio telescope has a diameter of $300\mathrm{m}$. Assume that it receives electromagnetic waves of wavelength $8.0\mathrm{cm}$. Determine if this radio telescope will see the Andromeda galaxy (a distance of $2.5\times {10}^6$light year away) as a point of source of light or an extended object. Take the diameter of Andromeda to be $2.2\times {10}^5$ light years. 

A spacecraft is returning to earth after a long mission far from earth. Estimate the distance from earth, at which an astronaut in the spacecraft will see first see the earth and the moon as distinct objects with a naked eye. Take the separation of the earth and the moon to be $3.8\times {10}^8\mathrm{m}$, and assume a pupil diameter of $4.5\mathrm{mm}$ and light of wavelength $5.5\times {10}^{-7}\mathrm{m}$.

The Hubble Space Telescope has a mirror of diameter $2.4\mathrm{m}$.

a. Estimate the resolution of the telescope, assuming that it operates at a wavelength of $5.5\times {10}^{-7}\mathrm{m}$.

The Hubble Space Telescope has a mirror of diameter $2.4\mathrm{m}$.

b. Suggest why the Hubble Space Telescope has an advantage over Earth-Based telescopes of similar mirror diameter.

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

a. The slit spacing $d$ of the grating.

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.

A diffraction grating is $5.0\mathrm{mm}$ wide and has $600 \mathrm{lines}$ per mm. A beam of light containing a range of wavelengths is incident on the grating. The average wavelength is $550\mathrm{nm}$. Determine the least wavelength range that can be resolved in the second order.

You can increase the resolving power by increasing the order $m$ or the number of lines $N$. Suggest whether these two ways are equivalent.