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.

HARD

12th Karnataka Board

IMPORTANT

Earn 100

A reflecting telescope has a concave reflector of radius of curvature $100 cm$ . Calculate focal length of eye piece to have a magnification of $10$ .

Important Questions on Ray Optics and Optical Instruments

HARD

12th Karnataka Board

IMPORTANT

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 ?

EASY

12th Karnataka Board

IMPORTANT

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.

Question Image

EASY

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 .

MEDIUM

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?

MEDIUM

12th Karnataka Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 9 - Ray Optics and Optical Instruments>Exercise>Q 32

Why is the aperture of the objective lens greater than that of the eyepiece in a telescope?

MEDIUM

12th Karnataka Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 9 - Ray Optics and Optical Instruments>Exercise>Q 33

Use the mirror equation to deduce that:
A convex mirror always produces a virtual image independent of the location of the object.
[Note: This exercise helps you deduce algebraically properties of images that one obtains from explicit ray diagrams.]

MEDIUM

12th Karnataka Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 9 - Ray Optics and Optical Instruments>Exercise>Q 34

Use the mirror equation to deduce that:
the virtual image produced by a convex mirror is always diminished in size and is located between the focus and the pole.
[Note: This exercise helps you deduce algebraically properties of images that one obtains from explicit ray diagrams.]

EASY

12th Karnataka Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 9 - Ray Optics and Optical Instruments>Exercise>Q 35

What is focal plane of a spherical mirror?

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.

Important Questions on Ray Optics and Optical Instruments

Learn and Prepare for any exam you want !

A reflecting telescope has a concave reflector of radius of curvature $100 cm$ . Calculate focal length of eye piece to have a magnification of $10$ .