AS Daily A Level Physics question
A student investigates refraction using a rectangular glass block. They plot sin(i) on the vertical axis against sin(r) on the horizontal axis and obtain a straight line through the origin with gradient 1.50 when the block is in air. They then fully immerse the block in water (refractive index ≈ 1.33) and repeat the same plot (sin(i in water) vs sin(r in glass)). What gradient should they expect now?
Answer
The correct answer is B.
Correct: B — approximately 1.13. The gradient of sin(i) (vertical) against sin(r) (horizontal) equals the ratio for entry medium to glass; replacing air with water scales the gradient by 1/1.33, so 1.50 ÷ 1.33 ≈ 1.13 (e.g. 1.50 ÷ 1.33 ≈ 1.125). A This is the reciprocal-type error from swapping axes or inverting the ratio (taking water-to-glass rather than glass-to-water). B Uses the correct idea that the new gradient is the old gradient divided by the water’s refractive index. C Assumes the gradient is unchanged, ignoring that changing the incident medium changes the ratio of the sines. D Multiplies the old gradient by 1.33, a product/area-style mistake that confuses how gradients scale with medium change.