Retroreflective materials reflect light to enhance the visibility of clothing. One type of retroreflective material is made from small glass spheres partially embedded in a silver-coloured surface that reflects light. A ray of monochromatic light follows the path shown as it enters one of the glass spheres. (a) Calculate the refractive index of the glass for this light. (b) Calculate the critical angle for this light in the glass. (c) The light is reflected at point P. Complete the diagram below to show the path of the ray as it passes through the sphere and emerges into the air.

Scottish Highers Physics Refraction of Light: Retroreflective materials reflec

Retroreflective materials reflect light to enhance the visibility of clothing - Scottish Highers Physics - Question 10 - 2016

Question 10

Retroreflective materials reflect light to enhance the visibility of clothing. One type of retroreflective material is made from small glass spheres partially emb... show full transcript

Worked Solution & Example Answer:Retroreflective materials reflect light to enhance the visibility of clothing - Scottish Highers Physics - Question 10 - 2016

Step 1

Calculate the refractive index of the glass for this light.

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Answer

To calculate the refractive index (n) of the glass, we use Snell's Law, which states that
$n = \frac{\sin i}{\sin r}$
where (i) is the angle of incidence and (r) is the angle of refraction.

From the diagram, we have (i = 36^\circ) and (r = 18^\circ).
Substituting the values:
$n = \frac{\sin 36^\circ}{\sin 18^\circ}$
Using a calculator, we find:
$n \approx 1.9$
Thus, the refractive index of the glass is approximately 1.9.

Step 2

Calculate the critical angle for this light in the glass.

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Answer

The critical angle ((\theta_c)) can be calculated using the formula: $\sin \theta_c = \frac{1}{n}$
Substituting the value of the refractive index from part (a):
$\sin \theta_c = \frac{1}{1.9}$
Calculating this gives:
$\theta_c \approx 32^\circ$
Therefore, the critical angle for the light in the glass is approximately 32 degrees.

Step 3

Complete the diagram below to show the path of the ray as it passes through the sphere and emerges into the air.

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Answer

In the completed diagram, the path of the ray will emerge into the air approximately parallel to the incident ray.
The ray will refract at the glass-air boundary as it exits the glass sphere.

Retroreflective materials reflect light to enhance the visibility of clothing - Scottish Highers Physics - Question 10 - 2016

Worked Solution & Example Answer:Retroreflective materials reflect light to enhance the visibility of clothing - Scottish Highers Physics - Question 10 - 2016

Calculate the refractive index of the glass for this light.

Calculate the critical angle for this light in the glass.

Complete the diagram below to show the path of the ray as it passes through the sphere and emerges into the air.

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