Let's break down the assertion-reasoning questions you've presented, focusing on the principles of optics involved in each statement. Understanding these concepts will help clarify whether the assertions and reasons are true or false.
Examining the First Set of Statements
Assertion 1: A spherical lens with equal radii will not show dispersion.
This statement is false. Dispersion occurs when light passes through a medium and is separated into its constituent colors due to varying refractive indices for different wavelengths. A spherical lens, regardless of having equal radii, can still exhibit dispersion because it refracts light. The degree of dispersion depends on the material of the lens and the wavelength of light, not just the shape or symmetry of the lens.
Reason 1: Dispersion is shown by two refracting surfaces inclined at some angle to each other.
This statement is true. When light passes through two refracting surfaces that are inclined, it can indeed show dispersion. The angle between the surfaces can cause different wavelengths of light to refract at different angles, leading to the separation of colors. This is commonly observed in prisms, where white light is dispersed into a spectrum.
Analyzing the Second Set of Statements
Assertion 2: All the images produced by a pair of plane mirrors inclined at an angle and an object are at the same distance from a particular point.
This assertion is true. When you have two plane mirrors inclined at an angle, the images formed will be equidistant from the point where the two mirrors meet (the vertex). The angles of incidence and reflection ensure that the images maintain this symmetry, resulting in all images being equidistant from that point.
Reason 2: All images produced by a pair of plane mirrors and an object lie on an ellipse.
This statement is false. The images produced by two plane mirrors do not lie on an ellipse; rather, they are arranged in a linear fashion based on the angle of inclination. The images will appear in a series of reflections, and their positions can be calculated using geometric principles, but they do not conform to an elliptical path.
Summary of Findings
- First set: Assertion 1 is false; Reason 1 is true.
- Second set: Assertion 2 is true; Reason 2 is false.
In conclusion, understanding the principles of optics, such as refraction and the behavior of light with mirrors, is crucial in evaluating these assertions and reasons. Each statement reflects fundamental concepts that can be observed in practical scenarios, such as using lenses and mirrors in everyday applications.
