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Chapter 20: Problem 63

Select the correct alternative(s): (a) A convex lens may form a real image (b) \(R=2 f\) formula is applicable to only paraxial ray (c) A convex lens becomes less convergent when it is immersed in water (d) All of the above

Short Answer

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(d) All of the above

Step by step solution

01

Understanding of Convex Lens and Real Image

A convex lens can converge light rays to a focal point. When an object is placed outside the focal length of a convex lens, it forms a real and inverted image on the opposite side of the lens. Thus, statement (a) is correct.
02

Understanding Lens Formula and Paraxial Rays

The formula \( R = 2f \) relates the radius of curvature \( R \) to the focal length \( f \), assuming paraxial rays where the rays are nearly parallel to the principal axis. Thus, statement (b) is correct.
03

Analyzing Convergence in Different Mediums

The refractive index of water is lower than that of air, leading to a decrease in the refractive power of the convex lens. This results in the lens being less convergent when immersed in water. Thus, statement (c) is correct.

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Key Concepts

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

Convex Lens
A convex lens is a piece of transparent glass or plastic that is thicker in the middle than at the edges. It has a distinctive ability to bend incoming light rays so that they converge or come together. This happens because of the specific curvature of the lens surfaces. When parallel light rays from an object pass through a convex lens, they bend towards the central axis and meet at a point called the focal point.
  • Convex lenses are often used in devices like cameras, magnifying glasses, and eyeglasses.
  • They have positive focal lengths, meaning they converge light.
  • They form images that may be real or virtual, depending on the object's position relative to the focal point.
The convex lens's ability to form real and inverted images is particularly important in various optical applications. When an object is placed beyond the focal length, the lens can project a real image onto a screen or other surface.
Real and Inverted Image
A real image is formed when light rays converge and actually pass through a point, allowing the image to be projected on a physical medium like a screen. For a convex lens, when the object is situated outside the focal length, the light rays coming from it are bent towards each other and meet on the other side of the lens. This results in a real image.
  • Such images are inverted, meaning they appear upside down compared to the object's orientation.
  • Real images can be captured on film or digital sensors in cameras.
The formation of a real and inverted image shows the powerful capability of lenses to manipulate light, creating images that are both high quality and practical for various purposes.
Understanding this concept is essential for leveraging the use of lenses in scientific and daily applications.
Paraxial Rays
Paraxial rays are light rays that travel close to the principal axis of an optical system, such as a lens. These rays make small angles with the principal axis, which simplifies the calculations involved in optical physics as they minimize the effects of spherical aberration.
  • The paraxial approximation assumes that sin 胃 鈮� 胃, which is valid when angles are small.
  • For lenses, only paraxial rays are considered to produce ideal, predictable image formations using formulas that relate radius of curvature, focal length, and object distance.
Importantly, the formula \( R = 2f \) for the radius of curvature is particularly applicable to paraxial rays.
This means these rays maintain focus more accurately, contributing to clearer and more accurate imaging.
Refractive Index
The refractive index is a measure of how much a material can bend light. It affects how lenses converge or diverge light rays. The refractive index is determined by the speed of light in a vacuum divided by the speed of light in the medium or material.
  • Materials with a higher refractive index bend light more than materials with a lower refractive index.
  • The change in refractive index affects the focusing ability of lenses. For example, a convex lens in air behaves differently when submerged in water.
When a convex lens is placed in water, its refractive index relative to water is lower than when in air.
This decreases the lens's converging power, making it less effective at focusing light. Understanding the refractive index's influence on lens behavior helps in the design and application of optical systems.

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Most popular questions from this chapter

One face \(A C\) of the glass prism is silvered as shown and the principal section of a glass prism is an isosceles triangle \(A B C\) with \(A B=A C\). The \(\angle B A C\), if the ray incident normally on face \(A B\) and after two reflections, it emerges from the base \(B C\), perpendicular to it, is : (a) \(70^{\circ}\) (b) \(36^{\circ}\) (c) \(72^{\circ}\) (d) \(44^{\circ}\)

The power and type of the lens by which a person can see clearly the distant objects, if a person cannot see objects beyond \(40 \mathrm{~cm}\), are : (a) \(-2.5 \mathrm{D}\) and concave lens (b) \(-2.5 \mathrm{D}\) and convex lens (c) \(-3.5 \mathrm{D}\) and concave lens (d) \(-3.5 \mathrm{D}\) and convex lens

In a tank filled with water of refractive index \(5 / 3\), a point source of light is placed \(4 \mathrm{~m}\) below the surface of water. To cut-off all light coming out of water from the source, what should be the minimum diameter of a disc, which should be placed over the source on the surface of water ? (a) \(1 \mathrm{~m}\) (b) \(4 \mathrm{~m}\) (c) \(3 \mathrm{~m}\) (d) \(6 \mathrm{~m}\)

Due to increase of temperature of medium, refractive index will be: (a) decreased (b) increased (c) unchanged (d) none of these

The rising and setting of sun appear red because of : (a) refraction (b) reflection (c) diffraction (d) scattering
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