Refraction

- Microwave: Microwaves have wavelengths ranging from 1 mm to 1 m, which corresponds to option (a) 700 nm to 400 nm. - Visible light: Visible light has wavelengths ranging from 400 nm to 700 nm, which corresponds to option (b) 1 nm to 10 nm. - Ultraviolet: Ultraviolet light has wavelengths between 0.1 nm and 400 nm, which corresponds to option (c). - X-rays: X-rays have wavelengths between 0.1 nm and 1 nm, which corresponds to option (d). Thus, the correct matching is option (2).

For the given problem, we know the following information: - The angle of the prism is . - The angle inside the prism varies with time as . Using Snell’s Law and the fact that the sum of the angles inside a prism equals the angle of the prism, we can relate the change in the angles and . The variation of is linked to , and since , we can use the relationship between these angles to determine the functional dependence of over time. Thus, will vary as . Therefore, the correct answer is option (4): .

In a compound microscope, the objective lens forms a real and diminished image, which is then magnified by the eyepiece lens. The final image formed by the microscope is virtual and enlarged due to the converging nature of the eyepiece and the intermediate image formed by the objective. Thus, the correct answer is option (1): Virtual and enlarged.