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Ok two questions:
1) page 240 TBR physics II, light rays travel from the object to the human eye, always right? so n1sintheta1=n2sintheta 2 where theta 2 is the angle reaching the human eye?
b) In question 10.4 a, assuming the above is right, you double n1, therefore sintheta 2 has to double, but if this is true, why does the perceived coin location seem shallower? I just didn't understand their reasoning. "Why does your brain think that the coin lies on a direct path from your eye to the coin's apparent position" and how would this lead to a greater theta 2 means that the perceived coin location moves UP (shallower)?
2) For dispersion on page 244, it says the shorter the wavelength, the greater the bending after light hits a prism...i was trying to prove this to myself mathematically but just wanted to verify i'm doing this right:
using equation10.5 on page 238, n1/n2 = lambda 2/lambda 1, then let's take violet light which has a relatively short wavelength (400nm) as compared to red (750 nm), looking at violet light only, lamba 2 would be the wavelength coming out of the prism and lambda 1 would be in the prism, if lambda 2 decreases this should either be caused by an increase in n2 or a decrease in n1 (eq. 10.5) (but since the indicies don't change in a dispersion problem, they are fixed right?) the angles must adjust, therefore sintheta 2 has to increase or sintheta 1 has to decrease? So, b/c sin theta 2 has to increase and sin theta (increases from 0 to 90), violet light (with a relatively short wavelength as compared to red light) should refract more?
3) Is Malus's law important for the MCAT BS section in spectroscopy or PS (polarization) problems? I didn't see it on the list of topics.
Thanks guys!
1) page 240 TBR physics II, light rays travel from the object to the human eye, always right? so n1sintheta1=n2sintheta 2 where theta 2 is the angle reaching the human eye?
b) In question 10.4 a, assuming the above is right, you double n1, therefore sintheta 2 has to double, but if this is true, why does the perceived coin location seem shallower? I just didn't understand their reasoning. "Why does your brain think that the coin lies on a direct path from your eye to the coin's apparent position" and how would this lead to a greater theta 2 means that the perceived coin location moves UP (shallower)?
2) For dispersion on page 244, it says the shorter the wavelength, the greater the bending after light hits a prism...i was trying to prove this to myself mathematically but just wanted to verify i'm doing this right:
using equation10.5 on page 238, n1/n2 = lambda 2/lambda 1, then let's take violet light which has a relatively short wavelength (400nm) as compared to red (750 nm), looking at violet light only, lamba 2 would be the wavelength coming out of the prism and lambda 1 would be in the prism, if lambda 2 decreases this should either be caused by an increase in n2 or a decrease in n1 (eq. 10.5) (but since the indicies don't change in a dispersion problem, they are fixed right?) the angles must adjust, therefore sintheta 2 has to increase or sintheta 1 has to decrease? So, b/c sin theta 2 has to increase and sin theta (increases from 0 to 90), violet light (with a relatively short wavelength as compared to red light) should refract more?
3) Is Malus's law important for the MCAT BS section in spectroscopy or PS (polarization) problems? I didn't see it on the list of topics.
Thanks guys!
