/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 33 The shape of spot light produced... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

The shape of spot light produced when bright sunshine passes perpendicular through a hole of very small size, is: (a) square because hole is square (b) round because it is an image of the sun (c) round with a small pinumbra around it (d) square with a small pinumbra

Short Answer

Expert verified
(b) round because it is an image of the sun

Step by step solution

01

Understanding the Problem

We need to determine the shape of the light pattern produced when sunlight passes through a small hole, given the shape of the hole and the angle at which the sunlight passes through.
02

Recognizing the Role of the Sun

The sunlight passing through the hole is essentially unaltered in terms of its original shape, since the size of the hole is much smaller when compared to the distance to the sun. Therefore, the sunlight retains the sun's shape, which is round.
03

Considering Projection Concepts

When light passes through a small hole, it acts similarly to a pinhole camera, projecting an inverted image of the light source. Here, the light source is the sun, which is round.
04

Examining Options for Penumbra

A penumbra is a partial shadow found around the edges of a light source. A very small hole might not allow enough room for a noticeable penumbra effect, leading us to focus on the direct image shape rather than penumbra-related options.
05

Deciding the Answer

Given the analysis, the hole does not significantly alter the round shape of the sun's image due to its small size. As such, the correct answer is (b) round because it is an image of the sun.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Pinhole Camera
A pinhole camera is a simple device that demonstrates how light can project images through small openings. Imagine a tiny hole acting like the lens of a camera. This is how a pinhole camera works. Light from the outside world enters through the small hole, creating an inverted image on the opposite side. This happens because light travels in straight lines. When it hits the pinhole, it bends to form an image inside the camera.
  • Pinhole cameras don't use lenses or fancy technology.
  • They rely on the simplicity of light passing through a small opening.
  • Images formed are usually inverted.
This concept is essential in understanding how light patterns are created by small holes, like in the exercise with sunlight shining through a small hole.
Light Projection
When we talk about light projection, we mean how light travels and creates images. Light moves in straight lines and can pass through openings to project shapes or shadows. This principle is similar to the way slide projectors work. If you place a barrier with a shape cut out, light will only pass through the open parts, forming an image or shape on the other side.
Light projection is a key concept in many optical devices, including the pinhole camera. It explains why objects have shadows and how light behaves when not obstructed.
Understanding light projection helps us grasp how sunlight shining through a tiny hole projects a round image, replicating the light's source—the sun.
Image Formation
Image formation is the process where light converges to form an image after passing through a small aperture, like in our pinhole camera. The size of the opening and the distance to the light source deeply influences this.
In our original exercise, the sun acts as the light source, and the small hole acts as the aperture. Because the sun is very far away, light from the sun enters the hole in parallel lines. These parallel lines mean the shape of the hole doesn’t distort the sun's image much, resulting in a round shape when projected.
The image formed is directly related to the light's original shape—here, a round image of the sun, as it is captured by the small opening.
Shadow Formation
Shadow formation involves the creation of a dark area or spot when an object blocks light from a source. This happens because light travels in unidirectional lines until something stops it.
  • Shadows give us clues about the light source's shape and size.
  • The shape of the object influencing the shadow can dramatically change the shadow's appearance.
In the context of the exercise, when sunlight enters a tiny hole, it projects a circular light pattern even though the hole might be differently shaped.
This is because shadows also depend on the size and distance of the light source, which in this case is too far to affect the basic shape of the projected light pattern significantly.

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Most popular questions from this chapter

The position of \(1 \mathrm{~cm}\) tall object which is placed \(8 \mathrm{~cm}\) infront of a concave mirror of radius of curvature \(24 \mathrm{~cm}\) is: (a) \(24 \mathrm{~cm}\) (b) \(25 \mathrm{~cm}\) (c) \(26 \mathrm{~cm}\) (d) \(27 \mathrm{~cm}\)

If an object is placed between two plane mirrors. a distance \(2 b\) apart, the object is situated at mid-point between mirrors, the position of \(n^{\text {th }}\) image formed by one of the mirrors with respect to the object is: (a) \(n b\) (b) \(2 n b\) (c) \(3 n b\) (d) \(4 n b\)

A cubical room is formed with 6 plane mirrors. An insect moves along diagonal of the floor with uniform speed. The velocity of its image in two adjacent walls are \(20 \sqrt{2} \mathrm{~cm} / \mathrm{s}\). Then the velocity of image formed by the roof is : (a) \(20 \mathrm{~cm} / \mathrm{s}\) (b) \(40 \mathrm{~cm} / \mathrm{s}\) (c) \(20 \sqrt{2} \mathrm{~cm} / \mathrm{s}\) (d) \(10 \sqrt{2} \mathrm{~cm} / \mathrm{s}\)

A man of height \(1.8 \mathrm{~m}\) stands infront of a large vertical plane mirror. The distance of the image from the man if he stands at a distance of \(1.5 \mathrm{~m}\) from the mirror is : (a) \(1 \mathrm{~m}\) (b) \(2 \mathrm{~m}\) (c) \(3 \mathrm{~m}\) (d) \(4 \mathrm{~m}\)

A bullet of mass \(m_{2}\) is fired from a gun of mass \(m_{1}\) with horizontal velocity \(v .\) A plane mirror is fixed at gun facing towards bullet. The velocity of the image of bullet formed by the plane mirror with respect to bullet is: (a) \(\left(1+\frac{m_{2}}{m_{1}}\right)\) (b) \(\left(\frac{m_{1}+m_{2}}{m_{1}}\right) v\) (c) \(\frac{2\left(m_{1}+m_{2}\right)}{m_{1}} v\) (d) none of these

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