Reflection And Refraction

Step 1: Use Ohm's Law to relate voltage, current, and resistance.

Ohm's Law states:

where is the voltage, is the current, and is the resistance. Rearranging for :

Step 2: Substitute the given values.

Substitute and :

Final Answer: The resistance of the filament is , which corresponds to option .

The person cannot see objects clearly beyond 40 cm, which indicates that they are suffering from myopia (nearsightedness). In myopia, the far point of the eye is closer than infinity, and the corrective lens required is a concave lens (negative power) to diverge the incoming light so that it appears to come from the person's far point.

Step 1: Use the lens formula to find the focal length of the corrective lens.

The lens formula is:

where is the power of the lens in diopters (D), and is the focal length in meters. For a concave lens used to correct myopia, the focal length is negative.

The far point of the person is 40 cm (0.4 m), which means the image formed by the lens must be at the far point when the object is at infinity. Thus:

Step 2: Calculate the power of the lens.

Substitute into the formula for power:

Final Answer: The power of the lens required to correct the vision is , which corresponds to option .

Dispersion occurs because different colors of light (wavelengths) are refracted by different amounts when passing through a prism. The refractive index of the glass depends on the wavelength of light, with shorter wavelengths (e.g., violet and blue) being refracted more than longer wavelengths (e.g., red).

In the visible spectrum, green light has a shorter wavelength than red light. Since shorter wavelengths experience greater refraction, green light is dispersed more than red light in a glass prism.

Final Answer: The correct answer is .