A diffraction grating has resolving power R = avg/ = Nm. (a) Show that the corresponding frequency
Question:
A diffraction grating has resolving power R = λavg/Δλ = Nm.
(a) Show that the corresponding frequency range Δf that can just be resolved is given by Δf = c/Nmλ.
(b) From Figure show that the times required for light to travel along the ray at the bottom of the figure and the ray at the top differ by Δt = (Nd/c) sin θ.
(c) Show that (Δf/Δt) = 1, this relation being independent of the various grating parameters. Assume N >> 1.
Step by Step Answer:
a Since the resolving power of a grating is given by R2A2 and by Nm the range of wavelengths that ca...View the full answer
Fundamentals of Physics
ISBN: 978-0471758013
8th Extended edition
Authors: Jearl Walker, Halliday Resnick
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Using a few basic physics principles, you can impress your friends with a trick that makes a bottle disappear. For this experiment, you will need a mini plastic bottle, glycerin, a glass, and a funnel. First, open the bottle and pour some glycerin into it, then close the bottle tightly. Next, pour some water into the glass using a funnel. Place the mini bottle into the glass of water and it will look normal. This is because light travels through air faster than it travels through the glass and water, allowing our eyes to see the bottle inside the glass. However, when you fill the mini bottle with more glycerin, and pour glycerin into the glass, then put the glycerin filled bottle into the glass with glycerin in it. Half of the bottle that is submerged in the glycerin will become invisible as the light travels through glass and glycerin at the same speed, thus it does not bend and no refraction takes place, making the bottle invisible. This happens because both glass and glycerin have almost the same refractive index, which causes the speed of light to be the same in both mediums, causing no bending of light and making the bottle disappear.
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