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A laser beam is incident at an angle of $30.0^{\circ}$ to the vertical onto a solution of corn syrup in water. If the beam is refracted to $19.24^{\circ}$ to the vertical, (a) what is the index of refraction of the syrup solution? Suppose the light is red, with wavelength 632.8 $\mathrm{nm}$ in a vacuum. Find its (b) wavelength, (c) frequency, and (d) speed in the solution.

a. $1.52$

b. $\text { The wayelength of light in the solution is } \lambda_{n}=416 \mathrm{nm} \text { . }$

c. $4.74 \times 10^{14} \mathrm{Hz} \text { in air and in syrup }$

d. $\text { The speed of light in syrup solution is } 1.97 \times 10^{8} \mathrm{m} / \mathrm{s}$

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but a off the given problem incident angle we have incident angle is, ah, 30 degrees and the refracted angle refracted angle angle is ah, 19.24 from Snell's Law. We can write and one we have is the one so in to weaken right from snow boys. One time sign off a 30 divided by a sign off from 19 point before this gives us in to off 1.52 I'll be off the prevalent in the medium. Having refracting extend is given by development off a light in a vacuum divided by the front index of media. Then we can find Linda in for substituting the value for 1.52 So Linda and will become Linda and will become Linda. Not we have a 632.8 centimeter divide by 1.5 to this gives us 41 69 meter is the prevalent off light in there Media may be affecting. That's 1.52 s. So it is a solution. But see frequencies given by CD by my landlord or three times 10 to power. It is the speed of light. Linda. Lord, we have is 63 2.8, uh, times 10 to the power minus nine. Working in two meters. We have here frequency 4.74 times Tented our 14 hers, um then part C or D. Sorry. Ah, using and Snell's law, we can, right? And one sign that the one is equal to in to sign that too on one easily won. So sign 30 is equal to in two signed 19.24 from here and do will be signed 30 Do right by a sign 19.24. This gives us into off 1.517 from the question that is a refracting That's the speed of light in reckoned you have a speed of light in medium. Then we can find the speeding this Arab that absolution. This will be a speed off light divided by and to which is 1.5 17 some student value for C, which is three times into power. Eight. We get here the speed off light in desire to be one for 97 times 10 to the power eight meter per second