During a science-club demonstration, students send a narrow light beam through three transparent blocks and towards air. They rotate each block until no ray...
Question 1 Report
During a science-club demonstration, students send a narrow light beam through three transparent blocks and towards air. They rotate each block until no ray can be seen leaving its upper face. At this point the light is reflected inside the block, so the angle inside the material is its critical angle. Table 1 records the results. The students use the same laser, a clean dry surface and the same angle scale for each block. A fibre-optic cable uses repeated internal reflection to keep light energy inside its glass core. The table can help the students decide which material would be suitable for a cable that needs light to remain trapped easily.
| Material | Critical angle / degrees |
|---|---|
| Acrylic | 42 |
| Dense glass | 38 |
| Flint glass | 35 |
Table 1
(a) Which material has the greatest refractive index? [1]
(b) Calculate the refractive index of flint glass. Use n = 1 ÷ sin c, where c is the critical angle. [2]
(c) Explain why a ray in flint glass at an angle of incidence of 36 degrees can undergo total internal reflection at a flint glass-air boundary. [1]
Fig. 1 shows a laboratory setup used to compare the apparent depth of a coin in a beaker of water. The coin is fixed to the base. A pin is moved vertically beside the beaker until its tip appears to be at the same position as the image of the coin. The observer keeps one eye at the marked position and does not move the beaker. The glass wall is thin and is ignored in this model. The real depth is the distance from the water surface to the coin.
(a) What is meant by the apparent depth of the coin? [1]
(b) Which is greater, the real depth or the apparent depth? [1]
(c) What happens to the light ray as it leaves the water? [1]
(d) Sketch a dashed line backwards from the ray in air to show where the observer sees the coin. [1]
Answer Details
Critical angle investigation
(a) Flint glass has the greatest refractive index. For light entering air, a smaller critical angle corresponds to a greater refractive index; flint glass has the smallest critical angle, \(35^\circ\). [1]
(b) \[n=\frac{1}{\sin c}=\frac{1}{\sin 35^\circ}=1.74\]
The refractive index is 1.74 (allow about 1.7). [2]
(c) \(36^\circ\) is greater than flint glass’s critical angle of \(35^\circ\), so the ray can undergo total internal reflection at a flint glass-air boundary. [1]
Apparent depth
(a) The apparent depth is the depth at which the coin, or its image, appears to be. [1]
(b) The real depth is greater than the apparent depth. [1]
(c) As the ray leaves water and enters air, it refracts away from the normal. [1]
(d) The dashed line is the backward extension of the emergent ray. It locates a virtual image above the real coin. [1]
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