In a prism r 1 + r 2 = A and δ = i + e - A , when the prism is at the position of minimum deviation D m . Show that the refractive index of the material of the prism is: μ = sin A + D m 2 sin A 2 Also derive the expression for D m for small angled prism.

Given r 1 + r 2 = A and δ = i + e - A In case of the minimum value of angle of deviation there is only one value of incident angle. In such case we have, i 1 = i 2 = e and r 1 = r 2 = r . Therefore, in case of minimum deviation we have as given r 1 + r 2 = A or A = r + r or r = A 2 .............(1) And δ m = i + i - A or i = δ m + A 2 .....................(2) Using Snell's relation n = sin i sinr putting the values we have, from (1)a nd n = sin A + δ m 2 sin ( A 2 ) .............................................(A) This is the required relation. Thin prism: As we have In case of thin prism, the angle of prism A is small and by the Snell's relation, we have, sin i 1 = μsin r 1 or i 1 = μr 1 Since i 1 is small, r 1 is also small, hence, δ = i 1 + i 2 - A = μr 1 + μr 2 - A = μ ( r 1 + r 2 ) - A = μA - A . Or δ = ( μ - 1 ) A ................................................(B) This is the required relation.

You know the phenomenon of the scattering of light by atmospheric particles. Write a few lines about the blue colour of the sky and reddish colour of the sky in the morning as well as in the evening.

The blue colour of the sky. The cause of this phenomenon is due to scattering of light by the atmospheric particles e.g. gas molecules, dust etc. The scattering of light is inversely proportional to the fourth power of its wavelength. Since the blue light has the least wavelength, it scatters the most towards the sky and hence the sky appears blue to us. For this to happen, the particles should have their size comparable to the wavelength of the light, The clouds have a much bigger size and scatter light of all wavelengths and hence appear white. The reddish colour of the sky in the morning and in the evening: At sunrise and sunset, the Sun is very low in the sky, which means that the sunlight we see has travelled through a much thicker amount of atmosphere. The shorter wavelength blue light is scattered further, as the sunlight passes over a greater distance, Most of the blue and other shorter wavelengths are removed by scattering and we see the longer wavelength yellow and red light.

Draw a ray diagram of a compound microscope forming an inverted image of an object, Which lens in the compound microscope acts as a simple microscope? If f o = 1 c m , f e = 2 c m a n d L = 20 c m . ,calculate the total magnification of the microscope.

Ray diagram of a compound microscope. From the diagram, it is clear that the eyepiece acts as a simple microscope. It forms a virtual and erect magnified image of a real image formed by the objective. Given here the focal length of the objective f o = 1 cm . The focal length of the eyepiece f e = 2 cm . The length of the microscope L = 20 cm . The total magnification of a compound microscope is the product of the magnification by the objective and that by the eyepiece i.e. m = m o × m e = L f 0 × D f e , where D = 25 cm . , the least distance of clear vision ( at which the final image is formed). Substituting the given values,we get, m = 20 1 × 25 2 = 250 .

In a combination of lenses in contact, the power of first lens is + 2 · 5 D and the focal length of second lens is - 25 c m . Calculate the power or focal length of the lens combination.

Given, Power of first lens P 1 = 2 · 5 Dioptre Focal length of second lens f 2 = - 25 c m = - 25 100 m = - 1 4 m we know that Power = 1 f o c a l l e n g t h power of second lens P 2 = 1 f 2 P 2 = 1 - 1 4 P 2 = 4 D Total Power = P 1 + P 2 P = 2 · 5 + 4 P = 6 . 5 D

For refraction at a convex spherical surface of radius of curvature R from a medium of refractive index n 1 to medium of refractive index n 2 ( n 2 > n 1 ) , establish the relation: n v - n u = n 2 - n 1 R . What will be behaver of a convex lens of the refractive index 1 . 47 when it is immersed in a liquid of refractive index 1 . 47 ?

Figure shows the formation of image I of an object O on the principal axis of a convex surface with the centre of curvature C . As the aperture is small the length of N M will be taken to be nearly equal to the length of the perpendicular from the point N on the principal axis. For small angles (assuming paraxial rays) we have, tan ∠ NOM = NM OM . tan ∠ NCM = NM MC , tan ∠ NIM = MN MI From the figure, we have i = ∠ NOM + ∠ NCM = NM OM + MN MC and r = ∠ NCM + ∠ NIM = NM CM - MN MI Since angles are small their sine will be equal to the angles Applying Snell law n 1 i = n 2 r So we have n 1 OM + n 1 MC = n 2 MC + n 2 MI or n 1 OM + n 2 M I = n 2 MC + n 1 M C Using the sign convention OM = - u , MI = + v and MC = R We have n 1 - u + n 1 v = n 2 - n 1 R This is the required relation, A biconvex lens of glass having refractive index 1 . 47 is immersed in a liquid of the refractive index 1 . 47 It becomes invisible and behaves as a plane glass plate.

Draw a ray diagram to show the correction of a myopic eye.The near point of the person with the defective eye is 75 cm . from the eye. Find the power of lens required to see clearly at 25 cm

Diagram for the correction of myopic eye, Given the near point of the person 75 cm . The required near point is 25 cm . In this case, the near point u = - 25 cm , v = - 75 cm and f = ? is the image distance and the required point is the object distance hence substituting in the lens formula we get, 1 f = 1 v - 1 u = - 1 75 + 1 25 gives f = 75 2 = 37 . 5 cm The power of the lens required = 100 37 . 5 = 2 . 66 D .

Establish the relation between the focal length f and radius of curvature R

Consider a light ray BD parallel to the principal axis PC is incident on the concave mirror PD After reflection, it goes along DR passing through the focus F. Then ∠ BDC = ∠ DCF (alternate angle) and ∠ BDC = ∠ CDF (law of reflection) Hence, ∠ CDF = ∠ DCF Hence △ FDC is isosceles. Hence DF = FC If the aperture of the mirror is small, the point D is very close to the point P , then DF = PF Therefore, PF = FC or, PF + PF = PF + PC or 2 PF = PC or PF = 1 2 P Or f = 1 2 R , where f = focal length and R = radius of curvature.

E M B I B E

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 9 - Ray Optics and Optical Instruments>assam board-2020>Q 18

MEDIUM

12th Assam Board

IMPORTANT

Earn 100

Which optical device can produce optical dispersion and which property is responsible for the dispersion of light? Draw a diagram to show that it is possible to obtain white light again after dispersion.

Important Questions on Ray Optics and Optical Instruments

EASY

12th Assam Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 9 - Ray Optics and Optical Instruments>assam board-2018>Q 1

A myopic person uses a lens of power

- 1.25 D

. What is his far point?

EASY

12th Assam Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 9 - Ray Optics and Optical Instruments>assam board-2018>Q 2

A pair of stars of actual separation one minute of arc is observed with an astronomical telescope of magnifying power

100

. What will be the separation of the image of the pair in degree.

EASY

12th Assam Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 9 - Ray Optics and Optical Instruments>assam board-2018>Q 3

Draw the schematic diagram of a Cassegrain telescope.

MEDIUM

12th Assam Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 9 - Ray Optics and Optical Instruments>assam board-2018>Q 4

Deduce the equivalent focal length of two convex lenses of focal lengths $f_{1} and f_{2}$ , when placed in contact.

MEDIUM

12th Assam Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 9 - Ray Optics and Optical Instruments>assam board-2018>Q 5

"When monochromatic light is incident on a surface separating two media, the reflected and refracted light both have same frequency as incidence frequency" Is this statement is true? If yes. why? If you think it is not true, why>

MEDIUM

12th Assam Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 9 - Ray Optics and Optical Instruments>assam board-2018>Q 6

In between a fixed object and a fixed screen a convex lens can cast two images at two different positions of the lens. Taking this to be a true statement show that the product of the size of the images is equal to the square of the object size.

EASY

12th Assam Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 9 - Ray Optics and Optical Instruments>assam board-2019>Q 7

The sparkle of a diamond can be explained by which phenomenon of light ?

EASY

12th Assam Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 9 - Ray Optics and Optical Instruments>assam board-2019>Q 8

Draw a neat diagram to show lateral shift of a ray refracted through a parallel-sided slab. Indicate the lateral shift in the diagram by a
double-headed arrow.

Learn and Prepare for any exam you want !

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