Optics

Step 1: Use the refractive index formula.
Refractive index where c = speed of light in vacuum, v = speed in the medium.
Step 2: Substitute values.
.
Step 3: Perform calculation.
m s .
Step 4: Conclusion.
Thus, light travels at m/s in diamond.

Step 1: Understanding the concept of apparent depth.
When light passes from one medium to another (from liquid to air in this case), the apparent depth is smaller than the real depth due to the change in the speed of light. The relationship between the real depth and the apparent depth is given by: where is the refractive index.
Step 2: Calculating the ratio.
Given that the refractive index of the liquid is 1.5, the ratio of the real depth to the apparent depth is: Step 3: Conclusion.
The ratio of the real depth to the apparent depth is 1.5.

Step 1: Understanding light wave behavior.
When light enters a new medium, such as water from air, its speed changes, which affects its wavelength. However, the frequency of the light remains constant because the frequency is determined by the source of the light, not the medium.
Step 2: Analyzing the options.
(A) Wavelength: Incorrect — The wavelength changes as the speed of light changes in different media.
(B) Wavenumber: Incorrect — The wavenumber is inversely proportional to the wavelength and therefore changes.
(C) Frequency: Correct — The frequency of the light remains unchanged when it enters a new medium.
(D) Intensity: Incorrect — The intensity can change depending on the properties of the medium.
Step 3: Conclusion.
The correct answer is (C) Frequency, as the frequency of light remains constant when it enters a new medium.

Step 1: Understanding the simple microscope.
In a simple microscope, the lens is typically a convex lens. The focal length of the lens is greater than the least distance for clear vision, allowing for magnification of objects. The magnification increases as the focal length of the lens increases.
Step 2: Analyzing the options.
(A) a lens with negative power is used: Incorrect — Negative power would imply a concave lens, which is not typically used in simple microscopes.
(B) the focal length of the lens is less than the least distance for clear vision: Incorrect — This would result in a diminished image.
(C) the focal length of the lens is greater than the least distance for clear vision: Correct — This is the defining characteristic of a simple microscope, which provides magnification.
(D) magnification depends only on the focal length of the lens: Incorrect — While magnification is related to the focal length, other factors also affect it.
Step 3: Conclusion.
The correct answer is (C) the focal length of the lens is greater than the least distance for clear vision, which defines how a simple microscope works.