Light from luminous point at the bottom of the glass slab of thickness 3 cm strikes the upper surface.The rays which are totally reflected at the top surface outline a circle of radius 2.4cm. Find refractive index of glass.

Physics

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To find the refractive index of the glass, we need to apply the laws of reflection and refraction.

Let's visualize the situation:
- A luminous point is placed at the bottom of a glass slab.
- Light from the luminous point strikes the upper surface of the slab.
- Some of the light is refracted when it enters the glass slab, while some of it is reflected at the top surface of the slab.
- The rays that are totally reflected outline a circle of radius 2.4 cm.

To solve this problem, we can use Snell's law and the law of reflection.

1. Let's make some observations:
- The circle formed by the rays that are totally reflected is centered on the luminous point at the bottom.
- The radius of the circle is given as 2.4 cm.

2. Determine the angle of incidence at the top surface.
- Since the rays that are totally reflected outline a circle, the angle of incidence for each ray is equal to the angle of reflection.
- The radius of the circle is 2.4 cm, which is the perpendicular distance between the center of the circle and the point of incidence on the top surface.
- The thickness of the glass slab is given as 3 cm.
- Therefore, the angle of incidence at the top surface can be found using trigonometry:
sin(angle of incidence) = 2.4 cm / 3 cm

3. Find the angle of refraction.
- We can use Snell's law, which states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the refractive indices of the two media.
- In this case, the incident medium is air, which has a refractive index of approximately 1.
- Let's denote the refractive index of the glass as 'n':
sin(angle of incidence) / sin(angle of refraction) = 1 / n

4. Calculate the refractive index.
- We now have two equations: sin(angle of incidence) = 2.4 cm / 3 cm and sin(angle of incidence) / sin(angle of refraction) = 1 / n.
- By substituting the first equation into the second equation, we can solve for 'n':
(2.4 cm / 3 cm) / sin(angle of refraction) = 1 / n

By solving this equation, we can find the refractive index of the glass.