Wave Optics Test - 1

The correct answer is to and fro motion of the eye lens.

Key Points

• The human eye is one of the most valuable and sensitive sense organs.
• It uses light and enables us to see the colorful world around us.
• The human eye is more or less like a photographic camera.
• The lens system of the eye forms an image of an object on a light-sensitive screen.
• The eyeball is almost spherical in shape having a diameter of about 23 cm.

THE HUMAN EYE:

Additional Information

• The eye lens is a transparent, biconvex structure in the eye that provides the finer adjustment required to focus objects on the retina. 

• The width pupil is adjustable due to the action of ciliary muscles, this action controls the intensity of light entering the eye and ensures the to and fro motion of the eye lens.

CONCEPT:

Power of Lens: 

• The inverse of the focal length is known as the power of the lens.
  • It shows the bending strength for the light ray of the lens.
  • The unit of power of a lens is Dioptre when the focal length of the lens is taken in meter (m).

\(\Rightarrow P = \frac{1}{f}\)

where P is the power of the lens and f is the focal length of the lens.

• Concave lens: It is a diverging lens that diverges the parallel beam of light.
  • It can also gather light from all directions and project it as a parallel beam.
  • The focal length and power of the lens of the concave lens are negative.
  • It has a virtual focus from the diverging rays of light that seem to converge.
• Convex lens: The lens whose refracting surface is upside is called a convex lens.
  • The convex lens is also called a converging lens.
  • The focal length and power of the lens of the convex lens are positive.

EXPLANATION:

Given - Power (P) = +2D

• As the power of the lens is positive then the lens is convex and it is used in Hypermetropia or Farsightedness for its correction. Hence option 2 is correct.

CONCEPT:

• Huygen's Principle Definition: Every point on a wavefront is a source of wavelets. These wavelets spread out in the forward direction, at the same speed as the source wave. The new wavefront is a line tangent to all of the wavelets.

• Huygen’s Reflection: The tangent to these wavelets shows that the new wavefront has been reflected at an angle equal to the incident angle.
• This is known as the law of reflection

​i.e., angle of incidence = angle of reflection

• The direction of propagation is perpendicular to the wavefront, as shown by the downward-pointing arrows.

Explanation:

From the above equation, we can see that according to Huygen's principle for reflection of the plain waves the law of reflection can be expressed as

the angle of incidence = angle of reflection

Hence option 4 is correct among all

Additional Information

Concept:

Telescope: The instrument which makes the distant object appear nearer is called a telescope.

The telescope has two convex lenses- one of them is called an objective lens and another one is known as the eyepiece

The magnification of a telescope is given by:

M = f0/fe

Where f0  is the focal length of the objective and fe is the focal length of the eyepiece.

The distance between the two lenses is given by:

L∝ = f₀ + f_e

Calculation:

Given:

m = 9, L = 20 cm

Magnifying power is given by:

\(m = \frac{{{f_o}}}{{{f_e}}} = 9\)    ---(1)

Also, f₀ + f_e = 20 cm     ---(2)

On solving (1) and (2), we get:

f_o = 18 cm, f_e = 2 cm

CONCEPT:

Reflection of a plane wave by a plane surface:

• In figure (a) we consider a plane wave passing through a thin prism.
• Clearly, since the speed of light waves is less in glass, the lower portion of the incoming wavefront (which travels through the greatest thickness of glass) will get delayed resulting in a tilt in the emerging wavefront as shown in the figure.

     -----Figure (a)

• In figure (b) we consider a plane wave incident on a thin convex lens, the central part of the incident plane wave traverses the thickest portion of the lens and is delayed the most.
• The emerging wavefront has a depression at the centre and therefore the wavefront becomes spherical and converges to the point F which is known as the focus.
• From the above discussion, it follows that the total time taken from a point on the object to the corresponding point on the image is the same measured along any ray.
• For example, when a convex lens focuses light to form a real image, although the ray going through the centre traverses a shorter path, because of the slower speed in glass, the time taken is the same as for rays travelling near the edge of the lens.

     -----Figure (b)

• In figure (c) a plane wave is incident on a concave mirror and on reflection, we have a spherical wave converging to the focal point F.
• In a similar manner, we can understand refraction and reflection by concave lenses and convex mirrors.

     -----Figure (c)

EXPLANATION:

• When a convex lens focuses light to form a real image, although the ray going through the centre traverses a shorter path, because of the slower speed in glass, the time taken is the same as for rays travelling near the edge of the lens. Hence, option 3 is correct.

CONCEPT:

Human eye:

• The organ due to which we can see the world is called the human eye.
• It consists of a convex lens/converging lens and the image by the human eye lens forms at the retina.

EXPLANATION:

​Myopia:

• Myopia is the condition that a person cannot see distant objects clearly.
• It is also called near-sightedness.
• In myopia patients image is formed in front of the retina.
• Myopia can be corrected by the use of a concave lens.

​Hypermetropia:

• Hypermetropia is the condition that a person cannot see nearby objects clearly.
• It is also called a long site.
• In hypermetropia patients image is formed behind the retina.
• Hypermetropia can be corrected by the use of a convex lens.
• A Cylindrical lens is used to correct Astigmatism.

Key Points

CONCEPT:

• Wavefront: The locus of all particles in a medium, vibrating in the same phase is called waveFront.
  • The direction of propagation of light (ray of light) is perpendicular to the waveFront.
  • Every point on the given wavefront acts as a source of a new disturbance called secondary wavelets which travel in all directions with the velocity of light in the medium.
  • A surface touching these secondary wavelets tangentially in the forward direction at any instant gives the new wavefront at that instant. This is called a secondary wavefront.

• Spherical wavefront: In the case of waves traveling in all directions from a point source, the wavefronts are spherical in shape.
  • This is because all such points which are equidistant from the point source will lie on a sphere and the disturbance starting from the source S will reach all these points simultaneously.

• Plane wavefront: As a spherical or cylindrical wavefront advances, its curvature decreases progressively. So a small portion of such a wavefront at a large distance from the source will be a plane wave-front. 

EXPLANATION:

• If a plane wavefront is incident on a convex lens then the emergent wavefront will be spherical with focus. So option 3 is correct.

CONCEPT:

• Wavefront: The surface of the constant phase on the wave is called a wavefront.
• Huygens Principle: The principle gives the idea of understanding the wave property of light using the concept of water waves.
  • The wavelets are formed when light emerges out of sources. The first wavelets generated are called primary wavelets.
  • Each point on primary wavelets is considered as a new source, and wavelets generated from these sources act as secondary wavelets.

​

EXPLANATION:

From the basic features of the Huygens principle, it is clear that each point on the primary wavelet contributes to the formation of secondary wavelets.

So, Each point on the primary wavefront generates a secondary wavefront.

• The correct answer is Option 2 i.e Refraction.​

​CONCEPT:

• Refraction: When a ray of light passes from one medium to another it suffers a change in direction at the boundary of two media is called refraction.

• The change in direction because the speed of light travels at different speeds in different mediums.

 .

• Reflection of a light ray is the phenomenon in which the light ray changes the direction of propagation when it strikes a boundary between different media through which it cannot pass.

• Diffraction is a general phenomenon exhibited by all types of waves. It is the bending of the wave around the corner of the obstacle.
• Polarization of light or any other wave is the process in which all the planes except one are removed so that the wave has its vibrations only in one plane.

EXPLANATION:

• Refraction is the phenomenon observed when a ray of light passes from one medium to another (rarer to denser or denser to rarer). So option 2 is correct.

EXTRA POINTS:

• Refraction and Reflection phenomena show the particle nature of light.
• Diffraction and Polarisation phenomena show the wave nature of light.

CONCEPT:

• Eye helps us in visualizing objects and also helps us in light perception, color, and depth perception.
• The human eye consists of the following parts:
  • ​Sclera, cornea, iris, pupil, lens, retina, and optic nerve.

​​

• Resolving power: Resolving power is the ability of an instrument or an eye to clearly distinguish between two objects that are at a very close distance to one another.

EXPLANATION:

• The human eye can distinguish the two objects as close as 0.1 mm distance apart.
• So the resolving power of a human eye is 0.1 mm.

Additional Information

EXTRA POINTS:

Different parts of the eyes and their functions are shown in the table: