Problem 82 - Master Resource Book in JEE Main Physics

Question

A convex lens forms a real image of a point object placed on its principal axis. If the upper half of the lens is painted black, (a) the image will be shifted upward (b) the image will be shifted downward (c) the intensity of the image will decrease (d) the image will not be shifted

Step-by-Step Solution

Answer

(c) the intensity of the image will decrease.

Step 1: Understanding the Problem

We have a convex lens with a real image formed from a point object on its principal axis. The upper half of the lens is painted black. We need to determine how these changes affect the image location and intensity.

Step 2: Concept of Lens and Image Formation

For a convex lens, a real image is formed on the opposite side where the object is placed. The focal point and position are crucial for determining the sharpness and position of the image.

Step 3: Effect of Blocking Part of the Lens

When half of a lens is painted, the image formation properties such as position and size remain the same. However, the intensity of the image is affected since fewer rays pass through. Only the lower half forms the same image, but dimmer.

Step 4: Analyzing Shifts in Image

Since the lens' entire lower half still creates converging rays in the same manner as if the lens were whole, the image remains on its original axis without shifting up or down.

Step 5: Conclusion and Final Answer

Painting half of the lens affects the brightness/intensity but does not alter the position or orientation of the image. Therefore, the image will not shift.

Key Concepts

Convex Lens

Convex lenses, commonly referred to as converging lenses, are thicker at the center than at the edges. These lenses are pivotal in ray optics as they produce both magnifying effects and have the capability to form real images of objects placed on their principal axis. When parallel rays of light pass through a convex lens, they converge at a focal point on the opposite side. This focal point is crucial for image formation and is a fundamental property of the lens.
The principal axis of a lens is the line that passes through the center of the lens and is perpendicular to its surfaces. It is along this axis that, typically, experiments and exercises tend to focus when talking about image formation. Convex lenses can focus light to create clear, real images, unlike concave lenses which typically produce virtual images only.

Real Image Formation

In ray optics, a real image is one that can be projected on a screen because it is formed by the actual convergence of light rays. When a convex lens is used, it refracts (bends) incoming parallel light rays to converge at a point. This point is the real focal point on the opposite side of the lens.
To understand real image formation better, let's consider a simple setup: When an object is placed at a certain distance from a convex lens, the light rays emanate from the object, pass through the lens, and converge to form a real image on the other side. The size and orientation of the image depend on the distance of the object from the lens:

• If the object is beyond the lens' focal length, the image will be inverted and reduced or enlarged based on its position.
• If the object is exactly at the focal point, the rays emerging from the lens will be parallel and, theoretically, no image will be formed.

This characteristic of forming real, inverted images makes convex lenses essential in cameras, projectors, and even in our eyes.

Lens Obstruction Effect

When part of a lens is obstructed, like painting the upper half black, it doesn't eliminate the ability of the lens to form an image, but it does affect certain characteristics of the image it forms. This scenario often raises the question of how such an obstruction impacts the lens' performance.
In the case of a convex lens, if half of it is obstructed, like what happens when it's partially painted, several observations can be noted:

• The real image location remains unchanged because the role of the lens' lower half remains unaffected in tracking the object's light paths correctly to form the same focused point.
• However, the brightness or the intensity of the resulting image will decrease. This occurs because fewer light rays can pass through the lens. Thus, the image maintains the same position and dimensions but appears dimmer.

Overall, although the aesthetic or brightness of the image can suffer due to obstruction, the image’s precise formation concerning size and placement won't be affected if only part of the lens is blocked.