Ray Optics And Optical Instruments

Apparent depth: From original water layer: With new liquid of refractive index 1.5: Shift in microscope = old apparent depth − new apparent depth:

Lens Maker’s Formula:

The refractive index of a medium is given by the ratio of real depth to apparent depth: Here,
- Real depth =
- Apparent depth =
Thus, the refractive index of benzene is 1.5.

Step 1: Understand the relation for the angle of the prism.
In a prism, the total angle of the prism is related to the angles of refraction and at the two faces of the prism. The formula to calculate the angle of the prism is: Where:
is the angle of refraction at the first face of the prism,
is the angle of refraction at the second face of the prism.

Step 2: Apply the formula.
Thus, the angle of the prism is the sum of the angles of refraction at both the faces of the prism. Final Answer: The correct answer is .

Critical angle is given by , where is the refractive index.
Higher the wavelength of light, lower the refractive index, and hence higher the critical angle.
Among visible light, red light has the longest wavelength (≈700 nm) and thus the lowest refractive index.
Therefore, red has the highest critical angle of incidence.

The magnifying power of a telescope is given by: where is the focal length of the eye piece and is the focal length of the objective lens (the tube length of the telescope). From the problem, we are given that: Substituting into the equation: Solving for : Thus, the focal length of the eye piece is .