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.

Larger aperture of objective lens in an astronomical telescope _____

increases the resolving power of telescope.

decreases the brightness of the image.

increases the size of the image.

decreases the length of the telescope.

E M B I B E

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 6 - Ray Optics and Optical Instruments>Exercise>Q 64

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Given the velocity of light in quartz $= 1.5 \times 10^{8} m s^{- 1}$ and velocity of light in glycerine $(\frac{9}{4}) \times 10^{8} m s^{- 1}$ . Now a slab made of quartz is placed in glycerine as shown. What is the shift produced by slab?

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Important Questions on Ray Optics and Optical Instruments

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 6 - Ray Optics and Optical Instruments>Exercise>Q 65

To get three images of a single object, we should have two plane mirrors at an angle of

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 6 - Ray Optics and Optical Instruments>Exercise>Q 66

A converging lens is to project the image of a lamp 4 times the size of the lamp on a wall at a distance of 10 m from the lamp. The focal length of the lens is

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 6 - Ray Optics and Optical Instruments>Exercise>Q 67

The graph between angle of deviation

(δ)

and angle of incidence

(i)

for a triangular prism is represented by :

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 6 - Ray Optics and Optical Instruments>Exercise>Q 68

The angle of a prism is $30^{\circ}$ and its refractive index is $\sqrt{2}$ , also, one of its surface is silvered. At what angle of incidence should a ray be incident on one surface so that after reflection from the silvered surface, it retraces its path?

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 6 - Ray Optics and Optical Instruments>Exercise>Q 69

In the formation of the rainbow, the total internal reflection occurs at the _____ of the raindrop.

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 6 - Ray Optics and Optical Instruments>Exercise>Q 70

An optical fibre used for telecommunication works on the principle of _____.

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 6 - Ray Optics and Optical Instruments>Exercise>Q 71

Is ordinary reflection of light identical with total internal reflection? (Yes/No) _____.

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 6 - Ray Optics and Optical Instruments>Exercise>Q 72

The angle of a prism is

A

and the critical angle with respect to the surrounding medium is

θ_{c}

. Then there will be no emergent ray through the prism, whatever be the angle of incidence if then the angle of the prism is equal and greater than the double of _____.