4cmAs u= real depth /apparent depth 1.5=3/apparent depth Therefore apparent depth = 2cm in slab Then distance from person = 2+2 = 4cm

Answer:

To determine the distance of the ink spot when viewed through a glass slab, we need to consider the refraction of light at the interface between air and glass. The refractive index of the glass slab is given as 1.5, which means that light travels slower in the glass than in air.

Given:
Refractive index of glass slab (μ) = 1.5
Thickness of the glass slab (t) = 3 cm
Distance of the observer from the ink spot (d) = 5 cm

Step 1: Refraction at the Air-Glass Interface:
When light passes from air to glass, it changes direction due to the change in speed. Snell's law relates the angle of incidence (θ1) and the angle of refraction (θ2) with the refractive indices of the two media.

The formula for Snell's law is:
μ1 * sin(θ1) = μ2 * sin(θ2)

Since the observer is looking from above, the incident ray is perpendicular to the surface of the glass slab, so θ1 = 0°. Therefore, sin(θ1) = sin(0°) = 0.

Applying Snell's law, we can find the angle of refraction (θ2) when light enters the glass slab:
1 * 0 = 1.5 * sin(θ2)
0 = 1.5 * sin(θ2)

Since the sine of any angle cannot be greater than 1, sin(θ2) must be 0. Therefore, θ2 = 0°.

Step 2: Path of Light Inside the Glass Slab:
Since the angle of refraction (θ2) is 0°, the light ray does not bend further inside the glass slab. It travels parallel to the surface of the slab.

Step 3: Refraction at the Glass-Air Interface:
When light passes from glass to air, it again changes direction due to the change in speed. Using Snell's law, we can determine the angle of refraction (θ3) when light exits the glass slab.

μ2 * sin(θ2) = μ1 * sin(θ3)
1.5 * sin(0°) = 1 * sin(θ3)
0 = sin(θ3)

Since the sine of any angle cannot be less than -1 or greater than 1, sin(θ3) can only be 0. Therefore, θ3 = 0°.

Step 4: Path of Light in the Air:
After refraction at the glass-air interface, the light ray continues its path parallel to the surface of the slab.

Step 5: Distance of the Ink Spot:
To find the distance of the ink spot, we need to consider the path of the light ray. It travels parallel to the surface of the glass slab, so the distance traveled inside the slab is equal to the thickness of the slab.

Therefore, the distance of the ink spot will be equal to the distance of the observer from the slab plus the thickness of the slab:
Distance of the ink spot = d + t
Distance of the ink spot = 5 cm + 3 cm
Distance of the ink spot = 8 cm