# Finding angle of refraction given angle of incidence?

• Martin Hanna
In summary, the conversation was about solving a question involving the refractive index and the critical angle. The question asked to find the value of the angle DBM, which was determined to be 90 degrees. From this, it was concluded that C would be the critical angle. The critical angle was then calculated to be 48 degrees, which was used to find the refractive index using the formula N = 1/sin C. The conversation ended with a thank you for the help.
Martin Hanna
Can someone help me in solving this question ?

my attemp is sin42/sin 90 to get the refractive index then n =sin i/sin r to get c
and for b n=1/sinc

Welcome to PF!

Try to answer part (i) first by examining the diagram and using a little geometry.

Martin Hanna
Thanks for responding but i am trying but can't figure it out its probably right there in my face but i just can't see it yet

What is the value of the angle DBM shown below?

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• Nemo.png
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that would be 90 ?

Yes, I think that's what you are supposed to assume. The fisherman's net (at D) is assumed to be essentially at the surface of the water.

so there fore the angle of incidence is 90 so that means C would be a critical angle

Martin Hanna said:
so there fore the angle of incidence is 90 so that means C would be a critical angle
Yes. From the diagram, can you determine the value of the critical angle in degrees?

42 ? i doubt you can just determine it from looking at the diagram as the question asks to calculate it

Note that the line connecting point A to Nemo's eye is a straight line.

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• Nemo 2.png
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therefore c must be 180-(42+90)

Yes

well it makes sense because the answer is 48 and 48 is the critical angle of air-water boundary so now i find the refractive index 1/48

Why 1/48?

because there is a formula which says that N(Refractive index) = 1/ sin C(48) oh i see yeah I am suppose to sin the 48

Yes, good.

thank you very much

## 1. What is the formula for finding the angle of refraction given the angle of incidence?

The formula for finding the angle of refraction given the angle of incidence is sin θr = n1 sin θi / n2, where θr is the angle of refraction, θi is the angle of incidence, and n1 and n2 are the indices of refraction for the two materials.

## 2. How do I determine the indices of refraction for the materials?

The indices of refraction for different materials can be found in reference tables or by using a refractometer, a device specifically designed for measuring the index of refraction. The index of refraction is a measurement of how much a material bends light as it passes through it.

## 3. Can I find the angle of refraction without knowing the indices of refraction?

No, the index of refraction is a necessary component in the formula for finding the angle of refraction. Without this information, it is not possible to accurately calculate the angle of refraction.

## 4. Is the angle of incidence always equal to the angle of refraction?

No, the angle of incidence and the angle of refraction are only equal if the light is passing through the interface between two materials with the same index of refraction. In all other cases, the angle of incidence and the angle of refraction will be different.

## 5. Does the angle of incidence affect the angle of refraction?

Yes, the angle of incidence is directly related to the angle of refraction. As the angle of incidence increases, the angle of refraction will also increase. This relationship is described by Snell's Law, which is the formula used to calculate the angle of refraction.

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