Shouldn't the refracted ray be along the boundary here?

[Physical_Fire]

A glass cube is held in contact with a liquid and a light ray is directed at a vertical face of the cube. The angle of incidence at the vertical face is 42° and the angle of refraction is 27° as shown in the diagram. The light ray is totally internally reflected for the first time at P. Complete the diagram to show the path of the ray beyond P to the air and calculate the critical angle for the glass-liquid boundary.

Here is the image: .

In the answer scheme, the critical angle is given as 63°. If it is 63°, shouldn't the refracted ray travel along the boundary and not totally internally reflect, as total internal reflection occurs when the angle of incidence is greater than the critical angle? How is it possible when they are the same angle?

 

[Baluncore]

Welcome to PF.

Can we assume that the point P is the same as the point X ?

 

[Physical_Fire]

Yes, it was a typo from my part; I apologize. I fixed it.

 

[DragonSpear]

your question is about the refraction of light from the glass to the liquid and for the critical angle you gotta get an angle of incidence that makes the refractive angle 90 so yes they are supposed to go with the boundary

 

[Physical_Fire]

But in the image, the ray doesn't go along the boundary, and I have trouble visualizing it. How should it be drawn?

 

[A.T.]

...as total internal reflection occurs when the angle of incidence is greater than the critical angle?

Just make it "greater or equal" if that limiting case confuses you. When you approach it from below, it is when the refraction disappears. When you approach it from above, it is when the refraction appears.