A helium-neon laser beam has a wavelength in air of 633 nm. It takes 1.38 ns for the light to travel through 30 cm of an unknown liquid. What is the wavelength of the laser beam in the liquid?

Video transcript

Hey everyone. So this problem is dealing with the refraction of light. Let's see what it's asking us. A scientist conducts an experiment to determine the refractive index of a transparent optical cylinder. A di of laser beam with a wavelength of 980 nanometers in the air is directed through the cylinder and travels a distance of 1.25 m in 6.45 nanoseconds. Using this data, we're asked to calculate the wavelength of the laser inside the cylinder. Our multiple choice answers R A 632 nanometers B 948 nanometers C 980 nanometers or D 1470 nanometers. OK. So we are asked to calculate the wavelength we're given distance speed and the wavelength of a um laser beam. And so sorry, we're given the wavelength of the laser beam in air. And we're asked to find the wavelength of that laser beam inside the cylinder. So we can recall that the definition of speed V is equal to the distance divided by the time. And we also know that our refractive index equation gives us a relationship between speed and the refractive index where speed is equal to the speed of light divided by N are ARA index. We can also recall that the wavelength of the same um wave in a vacuum is equal to the refractive index multiplied by that wavelength in the medium. So combining these equations, we can recognize that we are asked to solve for the wavelength inside of the medium, the cylinder. And so we have LAMBDA M is equal to lambda V divided by N. And substituting for N, we have Lambda sub V multiplied by V divided by C. And then lastly substituting for V, we have Lambda in the vacuum multiplied by D divided by C multiplied by T. And from there, we have everything we need to solve for that wavelength inside of the cylinder. So our wavelength in air 980 nanometers multiplied by our distance. So I'm going to write this with this back into standard units. So 980 times 10 to the negative 9 m, the distance it traveled 1.25 m divided by our speed of light. That's a constant three times 10 to the 8 m per second multiplied by our time, which was given a 6.45 nanoseconds. So times 10 to the negative nine seconds, we plug that into our calculator and we get 6.33 times 10 to the negative 7 m. Now, when we look at our multiple choice answers. The closest one is answer choice A so that's 633 nanometers which is very close to 632 nanometers. This difference can be explained by doing the problem in multiple steps and rounding or simply taking it uh versus taking it all in one and not rounding throughout each step, combining your equations differently, things like that. And so it's really important to not get caught up in the difference between 633 nanometers and 632 nanometers when you're looking at multiple choice answers where clearly 632 nanometers um is the closest. Uh And so that's why a is the correct answer. So that's all we have for this one. We'll see you in the next video.