Question

You design an experiment consisting of two identical lasers and two identical photodetectors. Each detector is the same fixed distance away from the emitter of each laser. Light emitted from the first laser travels only through air before reaching the detector. Light emitted from the second laser first travels through a 6.54 m long column of ice before emerging in air and continuing to the detector. The index of refraction of ice is 1.309. The lasers each emit a pulse of light simultaneously. What will be the difference in the times of arrival of the two pulses at the detectors (in ns)?

Answer 1

Δt = 6.74 ns

Step-by-step explanation:

given,

refractive index of ice = 1.309

length of ice = 6.54 m

speed of light in air = 3 × 10⁸ m/s

`time = (distance)/(speed)`

`t_a = (6.54)/(3 * 10^8)`

`t_a = 21.8* 10^(-9)`

t a = 21.8 ns

Speed of light in ice =
`(c)/(n)`

=
`(3 * 10^8)/(1.309)`

`t_i = (6.54)/(3 * 10^8)* 1.309`

`t_i = 28.54 ns`

`\Delta t = t_i - t_a`

= 28.54 - 21.8

Δt = 6.74 ns