We often state that the speed of light in vacuum is about 3 × 10 8 m s and the average speed of sound in air is about 330 m s . Why do you think the term 'average' is used to describe the speed of sound in the air but not the speed of light in vacuum?

The distance that the sound waves travel in a given amount of time is called the speed of sound. The average speed of sound in the air is about 330 m s . We know that sound waves are mechanical waves, and they can only travel through matter. The speed of sound through dry air at 20 ° C is about 343 m s . The speed of sound may vary through other matter or other temperatures. Since, the speed of sound may vary according to the temperatures and medium, we use the term average to describe the speed of sound. The speed of the light is experimentally found to be constant. Hence, the term average is not required in describing the speed of light.

The figure shows a ray of light falling normally on the face AB of an equilateral glass prism having a refractive index 3 / 2 , placed in water of refractive index 4 / 3 . Will this ray suffer total internal reflection on striking the face AC? Justify your answer.

It is given that the glass prism is equilateral. μ p = 3 / 2 μ w = 4 / 3 Thus, ∠ A = 60 ° . Let us draw a normal to the face AC. From the geometry, we can see, the angle of incidence on the face AC is 60 ° . Thus, i = 60 ° . Let this angle be the critical angle i.e. i = i c . Then the refractive index of the prism in the air, μ = 1 sin i c = 1 sin 60 ° μ = 2 3 = 1 . 54 Now if the prism is placed in water then the refractive index of a prism with water, μ A = μ p μ w = 3 2 4 3 = 9 8 = 1 . 125 The total internal reflection at face AC, is possible only when μ < μ A . But from the results obtained above, we can see that μ > μ A ∴ 1 . 54 > 1 . 125 No total internal reflection takes place and the light ray gets refracted from the prism placed in water. Thus, we can conclude that for total internal reflection, in this case, the Critical angle should be greater than 60 ° .

An object is placed in front of a concave mirror. It is observed that a virtual image is formed. Draw the ray diagram to show the image formation and hence derive the mirror equation 1 f = 1 u + 1 v .

Ray diagram to show the formation of a virtual image by concave mirror: Derivation of mirror equation using the above ray diagram: ∆ C A ' B ' and ∆ C A B are similar triangles. Hence, we can write: A ' B ' A B = C B ' C B = C P + P B ' C P - B P .......(i) D N is equal to A B and is a normal on the principal axis. ∆ F D N and ∆ F A ' B ' are similar triangles. The incident rays are considered to be paraxial rays hence, D and P are very close. We can write: A ' B ' A B = F B ' F D = F P + P B ' F D = F P + P B ' F P .....(ii) Using the above equations and substituting the values according to the sign convention we get: C P + P B ' C P - B P = F P + P B ' F P - 2 f + v - 2 f + u = - f + v - f ⇒ - 2 f 2 - f v = 2 f 2 - f u - 2 v f = u v ⇒ f u + f v = u v f On dividing both sides by u v f we get: 1 u + 1 v = 1 f The above equation is the required mirror equation.

MEDIUM

12th Karnataka Board

IMPORTANT

Earn 100

Draw a ray diagram for a monochromatic ray refracting from a glass prism. Write the expression for refractive index of glass in terms of prism angle and angle of minimum deviation.

Important Questions on Ray Optics and Optical Instruments

MEDIUM

12th Karnataka Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 9 - Ray Optics and Optical Instruments>Exercise>Q 66

The distance between two point sources of light is

24 cm

. Where should a convex lens of focal length

9 cm

be placed so that the images of both the sources are formed at the same point?

HARD

12th Karnataka Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 9 - Ray Optics and Optical Instruments>Exercise>Q 67

Define Snell's Law. Using a neat labelled diagram derive an expression for the refractive index of the material of an equilateral prism.

HARD

12th Karnataka Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 9 - Ray Optics and Optical Instruments>Exercise>Q 68

Show the nature of the

i - 𝛿

curve for a prism. Analyse the curve to show that for any particular value of

𝛿

, the difference between the fixed values of

A = r_{1} + r_{2} = r + r

and

e

decrease with the decrease of

𝛿

and becomes zero for

𝛿

minimum.

MEDIUM

12th Karnataka Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 9 - Ray Optics and Optical Instruments>Exercise>Q 69

We often state that the speed of light in vacuum is about

3 \times 10^{8} \frac{m}{s}

and the average speed of sound in air is about

330 \frac{m}{s}

. Why do you think the term 'average' is used to describe the speed of sound in the air but not the speed of light in vacuum?

HARD

12th Karnataka Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 9 - Ray Optics and Optical Instruments>Exercise>Q 70

A luminous point A is inside a circular track. A ray emerges from A and after two reflections at the circle returns to A. If

α

be the angle of incidence, x the distance from the centre of the circle to A and Y the distance of the centre from the point D, where the ray in its course crosses the diameter through A, prove that tan

α

\sqrt{\frac{(x - y)}{(x + y)}} .

EASY

12th Karnataka Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 9 - Ray Optics and Optical Instruments>Exercise>Q 71

What are the different types of beam of lights?

MEDIUM

12th Karnataka Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 9 - Ray Optics and Optical Instruments>Exercise>Q 72

Find the angle of minimum deviation for a prism of refracting angle

A

and refractive index

(\cot A / 2)

HARD

12th Karnataka Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 9 - Ray Optics and Optical Instruments>Exercise>Q 73

Derive the equation for the angle of deviation produced by a prism and thus obtain the equation for the refractive index of material of the prism

Draw a ray diagram for a monochromatic ray refracting from a glass prism. Write the expression for refractive index of glass in terms of prism angle and angle of minimum deviation.

Important Questions on Ray Optics and Optical Instruments

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