Question

The diameter of the sun subtends an angle of ${{0.5}^{{}^\circ }}$ at the surface of the earth. A converging lens of focal length 100 cm is used to provide an image of the sun onto a screen. The diameter (in mm) of the image formed is nearly:
(A) 1
(B) 3
(C) 5
(D) 9

Answer 1

HintWe know that a lens is a transmissive optical device that focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (elements), usually arranged along a common axis. The two laws followed by a beam of light traversing through two media are: The incident ray refracted ray, and the normal to the interface of two media at the point of incidence all lie on the same plane. The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant.

Complete step by step answer A convex lens is called a 'converging lens' or 'positive lens'. When light passes through the lens, it bends the light rays towards each other. This lens is thick at the center as compared to the edge. It helps to magnify the things and make them look bigger. As the parallel rays converge, the convex lens is termed as a converging lens. The convex lens is curved towards the inside. It is used to correct longsightedness or hypermetropia. The human eye, camera, telescope, microscope etc. are some examples of the convex lens. It is called a positive lens because of its positive focal length nature.
A concave lens is called a 'Diverging lens' or 'Negative lens. The concave lens spreads out the light when it passes through the lens. An image cannot form on a screen in this case. A concave lens is exactly opposite to a convex lens. It is thin at the center and thick at the edge. Similarly, a concave lens is called diverging lenses because they cause parallel rays to diverge. The concave lens is curved towards the outside. Lights, flashlights, laser, binocular etc. are the examples of the concave lens. The concave lens is called a negative lens because of its negative length nature.
For such numerical of length of image, whether in lenses or in mirrors, remember the following formula:
$\mathrm{I}=\mathrm{f} \theta$
Where, $\theta$ should be in radians
$\therefore \mathrm{I}=100 \times \dfrac{1}{2} \times \dfrac{1}{57.3}$
=0.89cm or $9 \mathrm{mm}$

So, the correct answer is option D.

Note: It can be said that in physics, refraction is the change in direction of a wave passing from one medium to another or from a gradual change in the medium. Refraction of light is the most commonly observed phenomenon, but other waves such as sound waves and water waves also experience refraction. Reflection involves a change in direction of waves when they bounce off a barrier. Refraction of waves involves a change in the direction of waves as they pass from one medium to another. Refraction is an effect that occurs when a light wave, incident at an angle away from the normal, passes a boundary from one medium into another in which there is a change in velocity of the light. Light is refracted when it crosses the interface from air into glass in which it moves more slowly.