Revision: Light >> Refraction of Light at Plane Surfaces Physics (English Medium) ICSE Class 10 CISCE

The return of light in the same medium after striking a polished surface is called reflection of light.

Light rays that are parallel to the principal axis of a concave mirror converge at a specific point on its principal axis after reflecting from the mirror. This point is known as the principal focus of the concave mirror.

Refracted light is the part of light enters into the other medium and travels in a straight path but in a direction different from its initial direction and is called the refracted light.

The change in the direction of the path of light when it passes from one transparent medium to another transparent medium is called refraction. The refraction of light is essentially a surface phenomenon.

When travelling obliquely from one medium to another, the direction of propagation of light in the second medium changes. This phenomenon is known as refraction of light.

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Light changes its direction when going from one transparent medium to another transparent medium. This is called the refraction of light.

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The bending of the light ray from its path in passing from one medium to the other medium is called 'refraction' of light.

The refractive index of a medium is defined as the ratio of the speed of light in vacuum (or air) to the speed of light in that medium.

Materials that allow light to pass through completely are known as transparent materials.

Materials that are not able to allow light to pass through, are called opaque material.

It is defined as the ratio of the velocity of light in medium 1 to the velocity of light in medium 2.

The perpendicular distance XY between the path of the emergent ray BC and the direction of the incident ray OD is called the lateral displacement.

A prism is a transparent medium bounded by five plane surfaces with a triangular cross-section.

Critical angle is the angle of incidence in the denser medium corresponding to which the angle of refraction in the rarer medium is 90°.

When a ray of light propagates from a denser medium to a rarer medium, the angle of incidence for which the angle of refraction is 90° is called the critical angle.

A prism having an angle of 90° between its two refracting surfaces and the other two angles each equal to 45° is called a total reflecting prism.

Ray 2 shows partially reflected ray.

Consider a point object O kept at the bottom of a transparent medium (such as water or glass) separated from air by the surface PQ.

A ray of light OA, starting from the object O, is incident on the surface PQ normally, so it passes undeviated along the path AA'. Another ray, OB, starting along the object O, strikes the boundary surface PQ at B and suffers refraction.

Since the ray travels from a denser to a rarer medium, it bends away from the normal N'BN drawn at the point of incidence B on the surface PQ and travels along BC in air.

When viewed by the eye, the ray BC seems to originate from point I, which is the virtual image of O created by extending lines A'A and CB backwards.

Thus, any point seen from the air will appear to be at I, which is a lesser depth = AI than its actual depth AO.

Angle of incidence = ∠OBN'

Angle of refraction = ∠CBN

Since, AO and BN' are parallel and OB is transversal line, so

∠AOB = ∠OBN' = i

Similarly, IA' and BN are parallel and IC is the transversal line, so

∠BIA' = ∠CBN = r

In right-angle triangle BAO,

sin i = `(BA)/(OB)` and,

In right-angle triangle IAB,

sin r = `(BA)/(IB)`​

For refraction from medium to air, by Snell’s law

`""_mμ_a = sin i/sin r = ((BA)/(OB))/((BA)/(IB))`

⇒ `""_mμ_a = (IB)/(OB)` 

Hence, refractive index of medium with respect to air is,

`""_aμ_m = 1/(""_mμ_a) = (OB)/(IB)` 

The object is viewed from a point vertically above the object O, since point B is very close to the point A.

∴ IB = IA and OB = OA

Hence,

`""_aμ_m = 1/(""_mμ_a) = (OA)/(IA)`

⇒ `"Real depth"/"Apparent depth"`

• Refractive index (µ) = c / V, where c is the speed of light in vacuum and V is the speed in the medium.
• The refractive index of a medium is always > 1 because the speed of light in any medium is less than in a vacuum.
• If µ₁ = µ₂ or the angle of incidence = 0°, the ray of light passes undeviated.
• Wavelength in medium A′ = A / µ; wavelength decreases in denser medium and increases in rarer medium.
• Refractive index decreases with decreasing speed of light, and is maximum for violet light and minimum for red light.

• A thick glass plate produces multiple virtual images due to repeated partial reflections and refractions inside the glass.
• The second image (A₂) is the brightest because it is formed by strong reflection at the silvered back surface.
• Later images (A₃, A₄, A₅...) are dimmer due to multiple internal reflections and light loss at each stage.

• An object in a denser medium (such as water or glass) appears shallower when viewed from a rarer medium (such as air) due to refraction.
• Apparent depth < Real depth, and the ratio is given by:
  μ = \[\frac {\text{Real depth}}{\text{Apparent depth}}\]​
• Shift in position = Real depth – Apparent depth =
  Real depth × (1 − \[\frac {1}{μ}\])
• The shift is greater when:
  The refractive index of the medium is higher,
  The medium is thicker, or
  The wavelength is shorter (more for violet, less for red).
• These formulas are valid only when the object is viewed vertically from above.

• Stars twinkle due to changes in the air’s refractive index caused by temperature variations.
• The Sun appears higher in the sky at sunrise and lower at sunset due to atmospheric refraction, which bends its rays.
• A hidden coin becomes visible when water is added, as refraction bends light from the coin toward the eye.
• Objects under a glass slab or in water appear raised because light bends as it passes from a denser to a rarer medium.
• Water tanks appear shallow, and legs appear shorter in water because light bends away from the normal.

• A total-reflecting prism has angles of 90°, 45°, and 45° and is used to produce total internal reflection within the prism.
• A total-reflecting prism deviates a light ray by 90° or 180° without loss of intensity and is used in periscopes, binoculars, and cameras.
• A total reflecting prism can erect an inverted image without deviation and is used as an erecting prism in slide projectors.

• A 30°, 90°, 60° prism can deviate a light ray through an angle less than 60° using total internal reflection, when the incident ray enters normally on the face BC and strikes AC at 60°, which is greater than the critical angle (42°).
• A ray incident normally on the hypotenuse face below the foot of the perpendicular suffers total internal reflection at BC, and emerges bending away from the normal at AB, resulting in a deviation greater than 60°.

• A total internal reflecting prism is used instead of a plane mirror to deviate light by 90° in a periscope and 180° in a binocular or camera.
• A total reflecting prism gives 100% reflection, while a plane mirror reflects less due to refraction and absorption.
• The image formed by a total-reflecting prism is brighter and does not fade over time, unlike in a plane mirror, where silvering deteriorates.

• Mirage seen on hot roads or in deserts is a consequence of total internal reflection.
• An empty test tube in water shines like a mirror due to total internal reflection.
• A crack in a glass vessel often appears shiny because of total internal reflection.
• A diamond sparkles due to total internal reflection within its surfaces.
• Optical fibres use total internal reflection to transmit light signals without energy loss.