refraction question

[theonlytycrane]

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The answer is (B). I chose it over (A) based on reasoning, but I was wondering how to determine that blue light would be refracted more?

Blue light has a shorter wavelength than Red light, but also has a higher frequency. Index of refraction n = c / v. I believe that v is the same for both blue and red light (same medium). Is there a relationship that I'm missing?

 

[aalamruad]

View attachment 203794
The answer is (B). I chose it over (A) based on reasoning, but I was wondering how to determine that blue light would be refracted more?

Blue light has a shorter wavelength than Red light, but also has a higher frequency. Index of refraction n = c / v. I believe that v is the same for both blue and red light (same medium). Is there a relationship that I'm missing?

Different wavelengths of light refract differently. We generally don't notice it, since the difference is pretty small, but higher frequency waves (i.e. blue light) refract more than lower frequency waves (i.e. red light). That actually gives them different indices of refraction because they have slightly different velocities. That's why you see a rainbow when light goes through a prism!

 

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First let's think about this conceptually - When white light is sent through a prism, what happens?

It gets broken into R O Y G B I V due to the varying indices of refraction.

What causes these different indices of refraction?

When light moves from a vacuum, to a different medium, it slows down.

Index of refraction n = c / v
c = speed of light in a vacuum (constant)
v = speed of light in medium

v = f λ
λ = v/f (or c/f for light in a vacuum)

f = frequency. remains constant (different colors of light have different frequencies, but one color will have the same frequency even after going through a different medium)
λ = wavelength, which can change

So, which should have a higher index of refraction?

Above, lambda nought is initial wavelength. lambda is wavelength in the medium.
Frequency cancels out, since it is constant before and after going through a medium (we aren't comparing 2 colors, but 1 color before and after going through a medium)

No matter what, lambda will be less than lambda nought and travelling in a medium will be slower than in a vacuum.
Red light will have a larger wavelength than blue light.
So, red light will have a larger v than blue light.
So, red light will have an index of refraction closer to 1, compared to blue light.
The closer the index of refraction is to 1, the less the light will bend.
So, blue light will bend further than red light.