Astigmatism is a type of refractive error in which the eye does not focus light evenly on the retina. This results in distorted or blurred vision at any distance Other symptoms can include eyestrain, headaches, and trouble driving at night. If it occurs in early life, In this defect the cornea has unequal curvature in different directions Therefore, such a person can not focus simultaneously on horizontal and vertical lines At a time either of the lines is seen clearly This can be treated by using cylindrical lenses..

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.

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What is astigmatism?

Important Questions on Ray Optics and Optical Instruments

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12th Karnataka Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 9 - Ray Optics and Optical Instruments>Exercise>Q 24

Discus about astronomical telescope.

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12th Karnataka Board

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 9 - Ray Optics and Optical Instruments>Exercise>Q 25

A compound microscope has a magnification $30$ . The focal length of eyepiece is $5 cm$ . Assuming that the final image is formed at least distance of distinct vision Find the magnification produced by objective.

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 9 - Ray Optics and Optical Instruments>Exercise>Q 26

What should be the position of an object relative to a biconvex lens so that it behaves like a magnifying glass?

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 9 - Ray Optics and Optical Instruments>Exercise>Q 27

A reflecting telescope has a concave reflector of radius of curvature

100 cm

. Calculate focal length of eye piece to have a magnification of

10

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 9 - Ray Optics and Optical Instruments>Exercise>Q 28

The near-point of a person is at a distance of

200 cm

from his eyes. What spectacle should he use in order to read print

20 cm

away ?

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 9 - Ray Optics and Optical Instruments>Exercise>Q 29

The ratio of the magnifying power of a convex lens used as a simple microscope when it is used to throw an image at the least distance of distinct vision to the magnifying power when it is used to throw an image at infinity is $6 : 5$ If the focal length of the lens is $4.8 cm$ , find the least distance of distinct vision.

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12th Karnataka Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 9 - Ray Optics and Optical Instruments>Exercise>Q 30

A compound microscope is composed of an objective and an eyepiece of focal lengths

0.5 cm

and

1.5 cm

respectively. Assuming that the least distance of distinct vision is

25 cm,

calculate the spacing required between the objective and eyepiece in order that the magnification is

500 .

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12th Karnataka Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 9 - Ray Optics and Optical Instruments>Exercise>Q 31

If an astronomical telescope forms a clear image of a star, what will be the distance between the lenses?

What is astigmatism?

Important Questions on Ray Optics and Optical Instruments

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