A transparent rectangular block 3.0cm thick is placed on a black dot. The dot when viewed from above is seen 2.0cm from the top of the block. The refractive index of the material of the block will be?
To determine the refractive index of the material of the block, we can use the concept of apparent depth.
1. Start by defining the given values:
- Thickness of the block (t) = 3.0 cm
- Distance of the dot from the top of the block (d) = 2.0 cm
2. Apparent depth (d') can be calculated using the formula:
d' = t / refractive index (n)
3. Rearrange the formula to solve for the refractive index (n):
n = t / d'
4. Substitute the values into the equation:
n = 3.0 cm / 2.0 cm
5. Perform the calculation to find the refractive index:
n = 1.5
Therefore, the refractive index of the material of the block is 1.5.
To find the refractive index of the material of the block, we can use Snell's law. Snell's law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two media involved.
In this case, the light travels from air (assumed to have a refractive index close to 1) to the material of the block. Let's assume the refractive index of the block's material is "n".
Let's consider the incident ray of light coming from air and entering the block. The ray travels vertically downwards, hits the top surface of the block, and then refracts. The angle of incidence (θ₁) is the angle between the incident ray and the normal to the surface, and the angle of refraction (θ₂) is the angle between the refracted ray and the normal to the surface.
Since we are observing the dot from above the block, the apparent distance between the dot and the top surface of the block will be the distance traveled by the ray inside the block (3.0 cm) divided by the refractive index "n".
Using Snell's law: sin(θ₁) / sin(θ₂) = n
The incident angle (θ₁) can be calculated using trigonometry. It is the angle formed between the line connecting the dot and top surface of the block and the normal to the surface (since the line is vertical). In this case, sin(θ₁) = 2.0 cm / distance between the dot and the top surface.
Therefore, the refractive index of the material of the block (n) can be calculated as follows:
n = sin(θ₁) / sin(θ₂) = (2.0 cm / distance between the dot and the top surface) / (3.0 cm / distance between the dot and the top surface)
To calculate n accurately, we need to know the actual distances involved. Once we have the distances, we can substitute them into the above formula to find the refractive index of the material of the block.
I had the same question but for me, it was a multiple-choice and I remembered this question.
the answer is 3.0/2.0