Problem 67 - Master Resource Book in JEE Main Physics

Question

A photograph of the moon was taken with telescope. Later on, it was found that a housefly was sitting on the objective lens of the telescope, in photograph, (a) there is a reduction in the intensity of the image (b) there is an increase in the intensity of the image (c) the image of housefly reduced (d) the image of the housefly will be enlarged

Step-by-Step Solution

Answer

(a) There is a reduction in the intensity of the image.

Step 1: Understanding the Problem

The problem describes a scenario where a housefly is resting on the objective lens of a telescope while a photograph of the moon is taken. We need to determine how this affects the intensity and image characteristics in the photograph.

Step 2: Effect on Intensity

The presence of the housefly on the objective lens will block some of the light reaching the lens. This obstruction will lead to a reduction in the intensity of the light that forms the image, because less light from the moon can pass through the telescope to reach the camera.

Step 3: Analyzing the Housefly's Image

The telescope's lens is primarily focused on the distant object (the moon). Since the housefly is on the objective lens, it is not within the focus range where images are captured clearly. Instead of appearing as a sharp image, the housefly's shadow might be seen faintly or blurred on the photograph.

Step 4: Conclusion on Image Effect

Since the housefly's image is not the focus of the telescope lens, it will not form an enlarged or sharp image whether it's magnified or reduced. Due to the defocusing effect on objects so close to the lens, the housefly would not appear significantly enlarged in the photograph. Its shadow might be seen but will not be a focused image.

Key Concepts

Telescope Lens

The telescope lens acts as a gatekeeper for the light entering the telescope. It collects and focuses light from distant objects, such as stars, planets, or in this case, the moon. This lens, called the objective lens, plays a critical role in determining the quality and brightness of the image. The placement of the lens within the telescope determines how far away an object can be and still appear in sharp focus. This ability to collect and direct light precisely is what allows telescopes to magnify distant objects without losing detail. When anything obstructs this lens, like a housefly, it affects the overall performance of the telescope. Here's how the lens functions:

• Gathering Light: The larger the lens, the more light it can gather, making dim objects appear brighter.
• Focusing Light: The objective lens brings light rays to a focus at a point where an image is formed.
• Magnification: With the help of an eyepiece, the focused image can be magnified for clearer viewing.

A clear view through a telescope depends largely on a clean, unobstructed lens.

Image Formation

In telescopes, image formation relies heavily on the lens focusing light precisely onto a point called the "focal plane." This is where a clear and sharp image is created. The goal is to have all the light rays from the object focus at this exact point to ensure image clarity. When the housefly landed on the telescope's objective lens during the photograph, it partially blocked some of the incoming light. As a result, only part of the moon's light reached the focal plane. This created a shadow or partial blur rather than a distinct image of the fly itself. Key aspects of image formation:

• Focal Plane: The point where light rays converge to form the image.
• Sharpness: Depends on how well-focused the light at the focal plane is.
• Obstruction Effects: Blocking light slightly, like with a fly, can reduce image sharpness.

Thus, any obstruction in the path of light affects the final image formed through a telescope lens.

Light Intensity

Light intensity in optics refers to the amount of light energy that reaches a surface. In telescopes, it represents how bright the image appears when viewed or captured. The objective lens is crucial in maintaining high light intensity, and any obstruction can reduce the amount of light that reaches the camera or viewer. If there is an obstruction, like a housefly on the lens, less light from the moon can pass through to the lens. Consequently, the photograph taken through the telescope will have a lower intensity, appearing dimmer. Consider these points:

• Obstructed Lens: Reduces the amount of light getting through to form an image.
• Dimmer Images: Less light results in images that are not as bright as they should be.
• Image Quality: A clearer, brighter photo depends on maximum light transmission.

Reducing light intensity affects not only brightness but can also influence contrast and detail clarity.

Focus and Defocus in Telescopes

Focusing in telescopes is performed by adjusting the lens or mirror to bring an image into clear view. This process is essential for capturing sharp images of distant objects. However, when objects are too close to the lens, such as a housefly sitting directly on it, they become out of focus, also known as defocused. In the case of defocus:

• Close Objects: Household objects near the lens fall outside the focal range. This means they will not form a clear image.
• Blur or Shadow: Near objects may cast a blurry silhouette or shadow within the telescope's view.
• Affected Clarity: Crucial details lost due to improper focusing distance.

Thus, while telescopes excel at focusing on distant objects, they struggle with nearby ones. The close proximity of the housefly prevented it from appearing clearly on the photograph, demonstrating the importance of having a well-adjusted focus.