BPhO1 2023 Paper 1 Part h

h) A glass block, with a reflecting lower surface, is shaped as a rectangular slab but whose
left and right sides are curved in the shape of quarter circles of radius 𝑅, as shown in
Fig. 3. The base A ray of light enters horizontally from the left and passes out through
the right side of the block at the same height above the base. The length of the top plane
surface is ℓ.

If the depth of the block is 2.0 cm and the refractive index 𝑛 = 1.46, what would be the
minimum value of ℓ to satisfy this situation?


Isn't the length of the block irrelevant? the question never states at what height the ray enters, so if it enters at depth zero no refraction will occur and it passes straight through. Doesn't this satisfy all the conditions?

… Isn't the length of the block irrelevant?

… the question never states at what height the ray enters, …

… so if it enters at depth zero no refraction will occur and it passes straight through. Doesn't this satisfy all the conditions?

Without the relevant diagram or figure, how can we answer or explain it?
If height is not given, you can assume a value that will cancel out in the computation.
Again, without the relevant diagram or figure, I don’t really know for sure about the setup.
This can happen, but it may be a trivial case.
Upload the whole question instead of discarding important diagram or figure.
Or you can put a link in the thread that link to the question.

Sorry for the lack of a diagram. I can come to terms with the "correct" solution, which is where the ray after refracting takes on the steepest possible gradient, which is the critical angle. However the bit I think is a bit ambigious is that a ray travelling along the reflective surface would also emerge parallel to the incident ray. Is this a bit pedantic or is the question poorly designed?