Physics Class 11 Notes
Want to be prepared before exams?
Revise 11th Physics topics.In this lesson, we will be learning about refraction at spherical surfaces. We will discuss how light bends as it passes from one medium to another through a curved boundary.
This explains the behaviour of mirrors, lenses and other optical instruments such as microscopes, telescopes and cameras. Once you have learnt about spherical surfaces, start working on the NCERT exercise of Ray Optics and Optical Instruments.
A spherical surface is a portion of a sphere, like surface of a lens, which may be convex or concave. Refraction at spherical surface is the bending of light when it passes from one transparent medium to another through a curved boundary.
The basic principle behind refraction at spherical surface is the different refractive index and change in speed. All these factors cause the light to bend and are governed by the Snell's Law. This type of refraction mostly occurs in lenses and other optical instruments.
For your understanding, we are including a simulation that explains refraction at spherical surface:
Physics Class 11 Notes
Want to be prepared before exams?
Revise 11th Physics topics.Physics Class 12 Notes
Need to complete Physics chapters before exams?
Revise 12th Physics Notes.The sign convention for refraction at spherical surfaces is a set of rules that determines the signs of different quantities involved in the refraction of light through spherical surfaces. These are also known as the New Cartesian Sign convention. Let us take a look at each one:
Class 12 CBSE Notes
Worried about the pending board syllabus?
Revise 12th Class Notes.11th CBSE Notes
Class 11th topics left before exams?
Revise 11th CBSE notes.The formula for refraction at spherical surface is as follows: Let us take a look at each term used in the formula:
This refraction at spherical surface formula is used for determining the position and nature of the image which is formed by refraction at a spherical surface.
Let us take a look at the derivation of the expression of refraction at a single spherical surface:
Let us take a look at the step-by-step derivation of refraction at spherical surface.
First, we will apply Snell’s law:
sin i = sinr
For smaller angles, sin i ≈ i and sin r ≈ r,
so: i = r
As we look at the triangle JAQ, we notice that
Here, u is accompanied by a negative sign since it is measured opposite to the direction of light.
In △IAQ,
For a spherical surface:
Now, let us relate i, r and γ.
As it is visible from the image:
i = α+γ
r = β−γ
Let us substitute these in Snell's law, which will result in:
Let us now express α, β, and γ as h.
We will now simplify and solve for l by cancelling h from both the sides: We will now rearrange the above equation to obtain the final expression:
The following table gives a glance at important terminologies used in this topic:
Term |
Definition |
Pole |
The geometric center of a spherical surface . |
Center of Curvature |
The center of sphere which includes the spherical surface. |
Radius of Curvature |
The radius of the sphere. |
Object Distance |
Object’s distance from the pole. |
Image Distance |
Image’s distance from the pole. |
Real Image |
Image formed by convergence of refracted rays. |
Virtual Image |
Image formed by apparent divergence of refracted rays. |
Refracted Ray | The light ray that bends and travels through the second medium after refraction. |
Refractive Index | A dimensionless measure denoted by μ that indicates how much does a medium slow down light |
Spherical Surface | A curved surface which is a part of a sphere that has a constant radius of curvature. |
Refraction | The phenomenon in which the light bends as it passes from one medium to another medium with varying refractive indices. |
Class 12th Physics for CBSE board students must take a look at the following notes as well:
Name of Chapter |
Name of Chapter |
---|---|
Chapter 14 Semiconductor Electronics: Materials, Devices and Simple Circuits |
Class 12th NCERT solutions for Physics chapters have been shared below:
Name of Chapter |
Name of Chapter |
---|---|
Chapter 14 Semiconductor Electronics: Materials, Devices and Simple Circuits |
What is the formula for refraction at spherical surface from rarer to denser medium?
Whenever a light ray travels from a rarer medium to a denser medium through a spherical surface, relationship between object distance (u), image distance (v), radius of curvature (R) and refractive index ( and ) is given by refraction formula for spherical surfaces as follows.
Which among denser or rarer media has a higher refractive index?
When these two media are compared, then, it is evident that rarer medium has lower refracted index as compared to denser medium. Denser media like glass and water have higher refractive index whereas rarer medium like air and vacuum have lower refractive index. Due to this, the light will bend towards the normal when it travels from rarer to denser medium. On the other hand, light will bend away from normal when it travels from denser to a rarer medium.
How can you tell whether a medium has low or high index of refraction?
You can identify whether a medium has higher or lower refractive index through the three ways. The first step is to observe the direction of bending. In this case, if the light is bending towards the normal, the second medium has higher refractive index. If the light bends away from normal, first medium has higher index of refraction.
In the second method, you can use Snell's law. If the second angle is smaller than the first one, second medium has higher refractive index. In case the first angle is smaller than second one, first medium has higher index of refraction. The third method is critical angle method where, if the light undergoes total internal reflection at boundary, the first medium has higher refractive index.
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