Physics Refraction Question Please Help?

This is a poor question as there are 2 correct answers. Statement B is ALWAYS true becaue sin(55) is less than 1 but refractive index is always greater than one. But D is also true and is the required answer. Here's one way to approach the probalm

___________________________________

Since none of the light is refracted into the air, total internal reflection must be occuring, therefore 55deg must be equal to or greater than the critical angle (C).

Guess a value for C to make the logic easier to work through - anything under 55deg is fine - say 40deg.

Find refractive index with asumed value:

n = 1/sinC = 1/sin(40)) = 1.56

sin(55) = 0.82.

1/sin(55) = 1.22

Now check A, B, C and D using the values:

A 1.56 is NOT less than 1.22. A is false.

B 1.56 IS greater than 0.82. B is true - but see my comment at the beginning.

C 1.56 is NOT less than 0.82. C is false.

D 1.56 IS greater than 1.22. D is true; this is the required answer.

So the answer is D; but B is a true statement too.

Since no light is refracted, we can assume this is a total internal reflection question. For total internal reflection to occur, the incident angle of 55.0 degrees must be greater than or equal to the critical angle, which is given by sin(critical) = n(air)/n(glass)=1/sin[n(glass)].

It follows that n(glass) = 1/sin(critical)

If 55 degrees is just equal to the critical angle, then n(glass) = 1/sin(55)

Suppose instead that 55 degrees is greater than the critical angle. Then sin(55) > sin(critical), since for an angle between 0 and 90, the greater the angle, the greater the sine of that angle. In this case, 1/sin(critical) > 1/sin(55). Thus, n(glass) = 1/sin(critical) > 1/sin(55).

so for there to be total internal reflection with an incident angle of 55 degrees, the refractive index of the glass must be greater than or equal to 1/sin(55). The answer is D.

That relies upon even if the mild is travelling right into a medium of larger or decrease refractive index than the only that is travelling out of - operating example, travelling into glass from air, or out of glass into air. Specify which and then there'll be sufficient archives for an answer