Optical Instruments

Step 1: Understanding the Relationship Between Speed of Light and Refractive Index
The speed of light in a medium ( ) is related to the refractive index ( ) of the medium by: where:
- m/s (speed of light in vacuum),
- (refractive index of glass).
Step 2: Substituting the Given Values

Step 3: Rounding Off the Answer
Approximating to three significant figures:
Step 4: Conclusion
Thus, the speed of light in glass is m/s.

Step 1: Understanding the Magnifying Power of a Telescope
- A refracting telescope consists of two lenses:
- The objective lens, which collects light and forms an image.
- The eyepiece lens, which magnifies the image formed by the objective. - The magnifying power ( ) of a telescope in normal adjustment (final image at infinity) is given by: where:
- = focal length of the objective lens,
- = focal length of the eyepiece lens.
Step 2: Substituting the Given Values
- Given: - , - .
Step 3: Conclusion
Thus, the magnifying power of this telescope is 100.

Step 1: Understanding the Minimum Deviation Formula
For a thin prism, the formula for the angle of minimum deviation ( ) is: where:
- is the refractive index of the prism,
- is the angle of the prism,
- is the minimum deviation.
Step 2: Substituting the Given Values
Given: - , - .
Step 3: Calculating Minimum Deviation
Thus, the angle of minimum deviation is .

Step 1: Using the Refraction Formula for a Spherical Surface
The refraction formula for a spherical surface is given by: where:
- is the refractive index of the first medium (air, ),
- is the refractive index of the second medium (glass, ),
- is the object distance,
- is the image distance,
- is the radius of curvature.
Step 2: Substituting the Given Values
Since the object is at , the equation simplifies to: Since tends to infinity, the equation reduces to:
Step 3: Solving for
Rearranging the equation: Thus, the image distance is .

Step 1: Understanding Focal Length
The focal length ( ) of a mirror is related to its radius of curvature ( ) by the formula: where:
- is the focal length,
- is the radius of curvature.
Step 2: Plane Mirror as a Special Case
- A plane mirror can be considered as a spherical mirror with an infinite radius of curvature.
- That is, for a plane mirror:
Step 3: Final Calculation
Substituting in the focal length formula: Thus, the focal length of a plane mirror is infinity.