9.3-Refraction of Light

9.3-Refraction of Light Important Formulae

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Grade 10 → Science → Light-Reflection and Refraction → 9.3-Refraction of Light

Refraction of light is the bending of light rays as they pass from one medium to another, due to a change in their speed. This phenomenon is essential in understanding how lenses and optical devices work. The degree of bending depends on the angle of incidence and the refractive indices of the two media.

Basic Concepts

To understand refraction, several key terms must be defined:

  • Incident Ray: The incoming ray of light that strikes the boundary between two media.
  • Refracted Ray: The ray that is bent as it passes into the second medium.
  • Normal Line: An imaginary line perpendicular to the surface at the point of incidence.
  • Angle of Incidence (i): The angle between the incident ray and the normal.
  • Angle of Refraction (r): The angle between the refracted ray and the normal.
Snell's Law

Snell's Law quantifies the relationship between the angles of incidence and refraction and the refractive indices of the two media:

n1sin(i) = n2sin(r)

  • n1: Refractive index of the first medium.
  • n2: Refractive index of the second medium.

The refractive index is a measure of how much light slows down in a medium compared to a vacuum. It can be calculated as:

n = c / v

  • c: Speed of light in a vacuum (approximately 3 x 108 m/s).
  • v: Speed of light in the medium.
Types of Refraction

Refraction can be classified into two main types:

  • Partial Refraction: Occurs when light passes from one medium to another, and some light is reflected while some is refracted. This can be observed when light travels from air to glass.
  • Total Internal Reflection: This occurs when light travels from a denser medium to a less dense medium, and the angle of incidence exceeds the critical angle, resulting in all light being reflected back into the denser medium. This principle is used in optical fibers.
Critical Angle and Total Internal Reflection

The critical angle is the angle of incidence beyond which light cannot pass into the second medium but is entirely reflected. It can be calculated using:

sin(c) = n2 / n1

Where c is the critical angle. This phenomenon is significant in applications such as fiber optics and diamonds, where brilliant sparkle is achieved through multiple internal reflections.

Applications of Refraction

Refraction has several practical applications:

  • Lenses: Convex and concave lenses utilize refraction to focus or disperse light, forming images in cameras, glasses, and microscopes.
  • Optical Instruments: Instruments like telescopes and binoculars use refraction to magnify distant objects.
  • Prisms: Prisms disperse light into its constituent colors, demonstrating the spectrum of light.
Refraction in Everyday Life

Refraction can be observed in various everyday phenomena:

  • Objects Under Water: When you look at an object submerged in water, it appears to be at a different position due to refraction, making it seem closer than it actually is.
  • Mirages: Mirages are optical illusions caused by the refraction of light in layers of air at different temperatures, leading to the appearance of water on hot surfaces.
  • Rainbow Formation: Rainbows are formed when light is refracted and dispersed by water droplets in the atmosphere, creating a spectrum of colors.


K.Venkataramana, CC BY-SA 4.0, via Wikimedia Commons

9.3-प्रकाश का अपवर्तन (Refraction of Light)

प्रकाश का अपवर्तन वह घटना है, जिसमें प्रकाश की किरण किसी माध्यम से दूसरे माध्यम में प्रवेश करते समय अपनी दिशा बदलती है। यह परिवर्तन प्रकाश की गति में बदलाव के कारण होता है। जब प्रकाश एक माध्यम से दूसरे माध्यम में प्रवेश करता है, तो उसकी गति और दिशा दोनों में बदलाव होता है। यह घटना मुख्यतः दो माध्यमों के बीच के अपवर्तनांक पर निर्भर करती है।

अपवर्तन का अध्ययन करने के लिए सबसे सामान्य रूप से उपयोग किया जाने वाला नियम है स्नेल का नियम

स्नेल का नियम (Snell's Law): इस नियम के अनुसार, जब कोई प्रकाश की किरण एक माध्यम से दूसरे माध्यम में प्रवेश करती है, तो इस प्रक्रिया में अपवर्तन कोण (refracted angle) और अभ्यस्त कोण (incident angle) के बीच एक स्थिर अनुपात होता है। यह अनुपात दो माध्यमों के अपवर्तनांकों (refractive indices) पर निर्भर करता है। स्नेल का नियम इस प्रकार है:

n₁ sin θ₁ = n₂ sin θ₂

जहाँ,
n₁ = पहले माध्यम का अपवर्तनांक,
n₂ = दूसरे माध्यम का अपवर्तनांक,
θ₁ = प्रकाश की किरण का पहले माध्यम में अभ्यस्त कोण,
θ₂ = दूसरे माध्यम में अपवर्तित किरण का अपवर्तन कोण।

अपवर्तनांक (Refractive Index): किसी माध्यम का अपवर्तनांक, उस माध्यम में प्रकाश की गति के अनुपात को दर्शाता है, जब इसे वैक्यूम में प्रकाश की गति से तुलना की जाती है। इसका सूत्र इस प्रकार है:

n = c / v

यहाँ,
n = माध्यम का अपवर्तनांक,
c = वैक्यूम में प्रकाश की गति (approximately $3 \times 10^8$ m/s),
v = माध्यम में प्रकाश की गति।

जब प्रकाश किसी घने माध्यम से कम घने माध्यम में प्रवेश करता है, तो वह अपनी दिशा में मोड़ता है और वह अपवर्तित होता है। यदि प्रकाश कम घने से घने माध्यम में प्रवेश करता है, तो उसकी दिशा में अधिक बदलाव होता है।

प्राकृतिक उदाहरण: जब हम एक काँच की छड़ी को पानी में डुबोते हैं, तो वह छड़ी पानी में टूटती हुई दिखाई देती है। यह प्रकाश का अपवर्तन है, जहाँ प्रकाश की गति पानी में अधिक धीमी होती है, जिससे छड़ी का आकार टूटता हुआ प्रतीत होता है।

कांच से हवा में प्रकाश का अपवर्तन: कांच से हवा में प्रवेश करते समय प्रकाश की गति अधिक होती है। इस कारण प्रकाश की किरण हवा की दिशा में मुड़ जाती है। इसी प्रकार, जल से हवा में प्रकाश का अपवर्तन होता है जब जल से हवा में प्रकाश की गति बढ़ती है।

सामान्य परिकल्पना (General Observation): अपवर्तन का मुख्य कारण प्रकाश की गति में परिवर्तन है। जब प्रकाश एक माध्यम से दूसरे माध्यम में प्रवेश करता है, तो उसके साथ संबंधित दोनों माध्यमों के अपवर्तनांक का अंतर महत्वपूर्ण होता है। यह अंतर ही प्रकाश की दिशा को निर्धारित करता है।

A ray of light travelling in air enters obliquely into water. Does the light ray bend towards the normal or away from the normal? Why?

Solution:

Refraction of Light

When a ray of light travels from air into water at an oblique angle, it bends towards the normal. This bending occurs due to the change in speed of light as it moves from a less dense medium (air) to a more dense medium (water). In air, light travels faster than in water. According to Snell's Law, when light enters a denser medium, its speed decreases, causing the light ray to change direction towards the normal line. This phenomenon is an example of refraction, illustrating the interaction between light and different media.

Light enters from air to glass having refractive index 1.50. What is the speed of light in the glass? The speed of light in vacuum is 3 $\times$ 10$^8$ m s${–1}$.

Solution:

Speed of Light in Glass

The speed of light in a medium can be calculated using the formula:

v = c/n

where:

  • v = speed of light in the medium
  • c = speed of light in vacuum (3 × 108 m/s)
  • n = refractive index of the medium (for glass, n = 1.50)

Substituting the values:

v = 3 × 108 m/s ÷ 1.50 = 2 × 108 m/s

Thus, the speed of light in glass is 2 × 108 m/s.

Find out, from Table 9.3, the medium having highest optical density. Also find the medium with lowest optical density.

Solution:

Optical Density of Mediums

According to Table 9.3, the medium with the highest optical density is diamond, with an optical density of 2.42. This high value indicates that light travels more slowly in diamond compared to other mediums. Conversely, the medium with the lowest optical density is air, with an optical density of approximately 1.0003. This low value suggests that light travels fastest in air compared to denser mediums. The differences in optical densities illustrate how various materials affect the speed of light passing through them.

You are given kerosene, turpentine and water. In which of these does the light travel fastest? Use the information given in Table 9.3.

Solution:

Speed of Light in Different Mediums

In the context of the refractive index, light travels fastest in mediums with a lower refractive index. According to Table 9.3, the refractive indices for kerosene, turpentine, and water are approximately 1.44, 1.47, and 1.33 respectively. Since water has the lowest refractive index among the three, light travels fastest in water. Kerosene and turpentine, having higher refractive indices, slow down the speed of light compared to water. Thus, the comparative speeds indicate that water allows light to travel faster than both kerosene and turpentine.

The refractive index of diamond is 2.42. What is the meaning of this statement?

Solution:

Understanding the Refractive Index of Diamond

The refractive index of a material indicates how much light slows down and bends when it enters that material. For diamond, a refractive index of 2.42 means that light travels 2.42 times slower in diamond than in a vacuum. This high refractive index results in diamond's characteristic brilliance and sparkle, as it causes significant bending of light. The greater the refractive index, the more the light is refracted, contributing to the gem's ability to reflect and refract light in striking ways, enhancing its visual appeal.

Define 1 dioptre of power of a lens.

Solution:

Definition of 1 Dioptre of Power of a Lens

The power of a lens is defined as the reciprocal of its focal length measured in meters. One dioptre (D) is the power of a lens with a focal length of one meter. Mathematically, it is expressed as:

Power (P) = 1 / Focal Length (f)

where P is in dioptres and f is in meters. A lens with a positive focal length converges light and has positive power, while a lens with a negative focal length diverges light and has negative power. This concept is crucial in optics.

A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it. Where is the needle placed in front of the convex lens if the image is equal to the size of the object? Also, find the power of the lens.

Solution:

Convex Lens Image Formation

For a convex lens, when a real and inverted image is equal to the size of the object, the object is placed at twice the focal length (2f). Given that the image distance (v) is -50 cm (real images have negative distance), using the lens formula:

1/f = 1/v - 1/u

Let u = -2f. Therefore, substituting values, we get:

1/f = -1/50 + 1/(2f)

Solving gives f = 25 cm. Thus, the power of the lens (P) is:

P = 1/f (in meters) = 1/0.25 = +4D.

Find the power of a concave lens of focal length 2 m.

Solution:

Power of a Concave Lens

The power (P) of a lens is calculated using the formula:

P = 1/f

where P is in diopters (D) and f is the focal length in meters. For a concave lens, the focal length is negative. Given the focal length (f) of the concave lens is -2 m:

P = 1/(-2) = -0.5 D

Thus, the power of the concave lens is -0.5 diopters.