Ray Optics, also known as Geometrical Optics, is one of the most important chapters in Class 12 Physics. It deals with the study of light as a ray and explains various optical phenomena like reflection, refraction, dispersion, and the working of optical instruments. Understanding this chapter not only helps in board exams but also in competitive exams like JEE and NEET.
In this article, we will cover all the concepts in detail with notes so that students can easily revise them before exams.
Class 12 Physics Ray Optics and Optical Instruments Notes | Complete Guide
1. Basics of Ray Optics
What is Ray Optics?
Ray optics assumes that light travels in straight lines called rays. It neglects the wave nature of light and focuses on geometrical laws like reflection and refraction.
Assumptions in Ray Optics
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Light travels in straight lines in a homogeneous medium.
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The wavelength of light is much smaller than the dimensions of the objects involved.
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Laws of reflection and refraction apply to each light ray individually.
2. Reflection of Light
Laws of Reflection
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The incident ray, the reflected ray, and the normal at the point of incidence lie in the same plane.
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The angle of incidence (i) is equal to the angle of reflection (r).
Mathematically:
i=ri = r
Types of Reflection
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Regular Reflection: From a smooth surface like a mirror.
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Diffuse Reflection: From a rough surface, scattering light in many directions.
3. Plane Mirrors
Image Formation
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Image formed is virtual, erect, and of the same size as the object.
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The distance of the image behind the mirror equals the object distance in front of the mirror.
Lateral Inversion
The left and right sides appear reversed in the mirror image.
4. Spherical Mirrors
Types
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Concave Mirror: Converging mirror.
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Convex Mirror: Diverging mirror.
Important Terms
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Pole (P): Center of the mirror’s surface.
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Center of Curvature (C): Center of the sphere of which the mirror is a part.
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Principal Axis: Line joining C and P.
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Focus (F): Point where parallel rays converge or appear to diverge from.
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Focal Length (f): Distance between P and F.
Mirror Formula
1f=1v+1u\frac{1}{f} = \frac{1}{v} + \frac{1}{u}
where
u = object distance, v = image distance, f = focal length.
5. Refraction of Light
Laws of Refraction
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Incident ray, refracted ray, and normal lie in the same plane.
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Snell’s Law:
sinisinr=n21\frac{\sin i}{\sin r} = n_{21}
where n21n_{21} is the refractive index of medium 2 with respect to medil
6.Total Internal Reflection (TIR)
Conditions for TIR
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Light travels from denser to rarer medium.
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Angle of incidence is greater than the critical angle CC.
Applications
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Optical fibers
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Prisms in binoculars
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Diamond’s brilliance
7. Refraction Through a Prism
The deviation angle δ\delta and refractive index relation:
n=sin(A+δm2)sin(A2)n = \frac{\sin(\frac{A+\delta_m}{2})}{\sin(\frac{A}{2})}
where A = angle of the prism, δm\delta_m = minimum deviation.
8. Dispersion of Light
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Splitting of white light into its constituent colors (VIBGYOR).
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Red has the least deviation, Violet the most.
9. Lens and Lens Formula
Types of Lenses
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Convex Lens: Converging lens.
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Concave Lens: Diverging lens.
Lens Formula
1f=1v−1u\frac{1}{f} = \frac{1}{v} – \frac{1}{u}
Magnification
M=h′h=vuM = \frac{h’}{h} = \frac{v}{u}
10. Power of a Lens
P=100f(cm)P = \frac{100}{f(cm)}
Unit: Dioptre (D)
11. Combination of Lenses
For two lenses in contact:
1F=1f1+1f2\frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2}
12. Optical Instruments
a) Human Eye
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Cornea: Refraction
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Lens: Adjustable focal length
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Retina: Image formation
b) Defects of Vision
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Myopia: Corrected by concave lens.
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Hypermetropia: Corrected by convex lens.
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Astigmatism: Cylindrical lens used.
c) Microscope
Magnification formula for a compound microscope:
M=(Lfo)(Dfe)M = \left( \frac{L}{f_o} \right) \left( \frac{D}{f_e} \right)
d) Telescope
Magnification:
M=fofeM = \frac{f_o}{f_e}
13. Polarisation of Light
Unpolarised light → passes through polariser → Polarised light.
Applications: Sunglasses, 3D movies, LCD screens.
14. Huygens vs Ray Optics
Huygens explains wave nature; Ray optics uses geometrical approach.
Objective Questions on Ray Optics and Optical Instruments
Q1. Which of the following is a correct law of reflection?
a) Angle of incidence = Angle of deviation
b) Angle of incidence = Angle of reflection
c) Angle of incidence = Angle of refraction
d) None of these
Answer:
The correct answer is b) Angle of incidence = Angle of reflection. According to the law of reflection, the angle of incidence is always equal to the angle of reflection.
Q2. In a plane mirror, the image formed is:
a) Real, erect, and same size
b) Virtual, erect, and same size
c) Real, inverted, and enlarged
d) Virtual, inverted, and diminished
Answer:
The correct answer is b) Virtual, erect, and same size because a plane mirror always forms a virtual image behind the mirror at the same distance as the object.
Q3. The mirror formula is:
a) 1/f = 1/u + 1/v
b) 1/f = 1/v + 1/u
c) 1/f = 1/v – 1/u
d) None of these
Answer:
The correct answer is b) 1/f = 1/v + 1/u, where f = focal length, v = image distance, and u = object distance.
Q4. In concave mirrors, the focus lies:
a) Behind the mirror
b) At the center of curvature
c) In front of the mirror
d) None of these
Answer:
The correct answer is c) In front of the mirror because concave mirrors converge light rays in front of them.
Q5. The unit of refractive index is:
a) m
b) cm
c) No unit
d) m²
Answer:
The correct answer is c) No unit. Refractive index is a ratio and hence dimensionless.
Q6. Total internal reflection occurs when light travels from:
a) Rarer to denser medium
b) Denser to rarer medium
c) Both directions
d) None of these
Answer:
The correct answer is b) Denser to rarer medium with the angle of incidence greater than the critical angle.
Q7. The phenomenon responsible for the twinkling of stars is:
a) Reflection
b) Refraction
c) Dispersion
d) Scattering
Answer:
The correct answer is b) Refraction because light from stars bends due to atmospheric layers of different densities.
Q8. Which color of light has the least deviation in a prism?
a) Violet
b) Red
c) Blue
d) Green
Answer:
The correct answer is b) Red because red light has the longest wavelength and deviates the least.
Q9. The lens formula is:
a) 1/f = 1/v + 1/u
b) 1/f = 1/v – 1/u
c) 1/f = 1/u – 1/v
d) None of these
Answer:
The correct answer is b) 1/f = 1/v – 1/u for lenses, where sign conventions differ from mirrors.
Q10. The power of a lens is measured in:
a) Joule
b) Dioptre
c) Newton
d) Hertz
Answer:
The correct answer is b) Dioptre (D). Power = 100 / focal length in cm.
Q11. The focal length of a convex lens is positive because:
a) It diverges rays
b) It converges rays
c) It produces virtual images
d) It is a plane lens
Answer:
The correct answer is b) It converges rays to a point on the principal axis.
Q12. Myopia can be corrected by using:
a) Convex lens
b) Concave lens
c) Cylindrical lens
d) Bifocal lens
Answer:
The correct answer is b) Concave lens because it diverges light before it enters the eye.
Q13. The human eye lens is:
a) Concave
b) Convex
c) Plane
d) Diverging
Answer:
The correct answer is b) Convex as it converges light on the retina.
Q14. A telescope is used to view:
a) Distant objects
b) Nearby objects
c) Both a and b
d) None of these
Answer:
The correct answer is a) Distant objects because telescopes have large focal length objective lenses.
Q15. The magnifying power of a microscope increases when:
a) Focal length of objective decreases
b) Focal length of eyepiece decreases
c) Both a and b
d) None of these
Answer:
The correct answer is c) Both a and b because shorter focal lengths give higher magnification.
Q16. Polarisation proves:
a) Light is a wave
b) Light is a particle
c) Light is both wave and particle
d) Light is neither wave nor particle
Answer:
The correct answer is a) Light is a wave because only transverse waves can be polarised.
Q17. In dispersion of light through a prism:
a) Speed of all colors remains same
b) Speed of all colors changes equally
c) Speed of each color changes differently
d) None of these
Answer:
The correct answer is c) Speed of each color changes differently, leading to separation of colors.
Q18. The angular magnification of a simple microscope is given by:
a) 1 + D/f
b) D/f
c) 1 – D/f
d) f/D
Answer:
The correct answer is a) 1 + D/f, where D = least distance of distinct vision, f = focal length.
Q19. The critical angle depends on:
a) Wavelength of light
b) Refractive index
c) Both a and b
d) None of these
Answer:
The correct answer is c) Both a and b because refractive index and wavelength affect total internal reflection.
Q20. The resolving power of a telescope increases with:
a) Decrease in aperture
b) Increase in aperture
c) Focal length increase
d) None of these
Answer:
The correct answer is b) Increase in aperture because a larger aperture allows more light and better resolution.
Short Answer Questions Ray Optics and Optical Instruments
Q1. What is lateral inversion in a plane mirror?
Answer:
Lateral inversion is the phenomenon where the left side of the object appears as the right side in the image and vice versa. This happens because of the way light reflects off the plane mirror.
Q2. Define critical angle.
Answer:
The critical angle is the angle of incidence in the denser medium for which the angle of refraction in the rarer medium becomes 90°. Beyond this angle, total internal reflection occurs.
Q3. What is dispersion of light?
Answer:
Dispersion is the splitting of white light into its constituent colors (VIBGYOR) when it passes through a prism. It occurs because different colors of light have different speeds in the medium, leading to different angles of refraction.
Q4. Give two differences between convex and concave lenses.
Answer:
A convex lens converges parallel rays to a point and has a positive focal length, whereas a concave lens diverges parallel rays and has a negative focal length. Convex lenses form real or virtual images, while concave lenses form only virtual images.
Q5. What is the significance of polarisation of light?
Answer:
Polarisation proves that light waves are transverse in nature. It is used in sunglasses, 3D movies, LCD screens, and stress analysis in materials.
Long Answer Questions Ray Optics and Optical Instruments
Q1. Explain the laws of reflection and derive the mirror formula.
Answer:
The laws of reflection state that (i) the incident ray, the reflected ray, and the normal at the point of incidence all lie in the same plane, and (ii) the angle of incidence equals the angle of reflection. For deriving the mirror formula, consider a concave mirror with object distance uu, image distance vv, and focal length ff. Using similar triangles formed by the rays and the principal axis, we derive the relation:
1f=1v+1u\frac{1}{f} = \frac{1}{v} + \frac{1}{u}
This is known as the mirror formula, applicable for both concave and convex mirrors with proper sign conventions.
Q2. Describe the phenomenon of total internal reflection with its conditions and applications.
Answer:
Total internal reflection (TIR) occurs when light travels from a denser medium to a rarer medium, and the angle of incidence exceeds the critical angle. At this point, light is completely reflected back into the denser medium. Applications include optical fibers for communication, prisms in periscopes, binoculars, and the sparkle of diamonds. TIR ensures maximum light transmission without loss, making it useful in many optical devices.
Q3. Explain the working of a compound microscope with its magnification formula.
Answer:
A compound microscope uses two lenses—an objective lens and an eyepiece lens. The objective lens forms a real, inverted, and magnified image of the object. This image acts as the object for the eyepiece, which further magnifies it to produce a final virtual, erect image. The magnification of a compound microscope is given by:
M=(Lfo)(Dfe)M = \left( \frac{L}{f_o} \right) \left( \frac{D}{f_e} \right)
where fof_o = focal length of objective, fef_e = focal length of eyepiece, LL = tube length, and DD = least distance of distinct vision.
Q4. Derive the expression for the refractive index using a prism in the minimum deviation position.
Answer:
Consider a prism with an angle AA and a ray of light passing through it. When the angle of deviation δ\delta is minimum, the incident ray and emergent ray make equal angles with the prism. Using geometry of the prism and Snell’s law, the refractive index nn is given by:
n=sin(A+δm2)sin(A2)n = \frac{\sin \left(\frac{A + \delta_m}{2}\right)}{\sin \left(\frac{A}{2}\right)}
where δm\delta_m is the minimum deviation. This formula is used in experiments to find the refractive index of prism material.
Q5. Discuss the construction and working of an astronomical telescope.
Answer:
An astronomical telescope consists of two lenses: the objective lens (large focal length) and the eyepiece lens (small focal length). The objective lens collects light from distant objects and forms a real, inverted image at its focus. The eyepiece magnifies this image to form a virtual, inverted image. The angular magnification of a telescope is given by:
M=fofeM = \frac{f_o}{f_e}
where fof_o is the focal length of the objective and fef_e of the eyepiece. It helps in viewing distant objects like stars and planets.
Conclusion
Ray Optics and Optical Instruments form the foundation for understanding light behavior in real life. Mastery of formulas, diagrams, and applications ensures success in exams and builds a base for advanced optics studies.
We are Completed Ray Optics and Optical Instruments Notes And important Questions.
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