(a) Why do we use red colour as a danger signal on the top of a skyscraper?

(b) The diagram below shows the path of a blue ray through the prism :

1. Calculate the critical angle of the material of the prism for blue colour.
2. What is the measure of the angle of this prism (A)?
3. Which colour should replace the blue ray, for the ray to undergo Total Internal Reflection?

(a) Red colour is used as a danger signal on the top of a skyscraper because red light has the longest wavelength among visible light, so it is scattered the least by air molecules and dust and remains visible from a long distance and in low visibility, making it ideal for danger signals.

(b)

1.

Here, the refracted ray PQ is normal to the surface AB of the prism (i.e., ∠r = 0°), so the incident ray at the point P should also be normal to the surface AB so that ∠i = 0°.

At point Q, the angle of incidence for the ray PQ = 133° - 90° = 43°

Now, this angle should be equal to the critical angle because ray PQ is refracted at 90°, i.e., it is refracted along QC. Hence, the critical angle of the prism is 43°.

2. In △AРQ

∠APQ + ∠PQA + ∠PAQ = 180°

⇒ 90° + 47° + ∠PAQ = 180°

⇒ ∠PAQ = 180° - 90° - 47°

⇒ ∠ PAQ = 43°

Hence, ∠A= 43°

3. As the light used and its wavelength determine the angle of deviation since with a decrease in the light wavelength, the angle of deviation increases so the beam will experience total internal reflection if we swap out the blue light with lower wavelength i.e., indigo.