Have you ever wondered why a pencil bends when half immersed in water? Or why does a spoon appear deformed in a glass of water? These fascinating events can be described using ray optics techniques. Ray optics, often known as geometrical optics, is a branch of optics class 12 that studies how light behaves while travelling in straight lines or rays.
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The formation of rainbows is another interesting real-life example that can be described by ray optics. When sunlight passes through water droplets in the air, it is reflected and refracted, causing colour dispersion and the formation of a circular arc of colours known as a rainbow. Understanding ray optics principles allows us to understand how different colours are generated and why rainbows occur at specific angles relative to the observer.
Topics and sub-topics of Ray Optics And Optical Instruments are listed below:
Ray optics (or geometrical optics) deals with the study of light using the concept of rays. It explains reflection, refraction, formation of images by mirrors and lenses and the working of optical instruments like microscopes and telescopes.
When light rays fall on a smooth spherical surface, they get reflected following the laws of reflection. Spherical mirrors are of two types:
According to the New Cartesian Sign Convention:
The relation between object distance $(u)$, image distance $(v)$, and focal length $(f)$ is:
$
\frac{1}{f}=\frac{1}{v}+\frac{1}{u}
$
Refraction is the bending of light when it passes from one medium to another due to a change in speed.
When a ray of light travels from a denser medium to a rarer medium, beyond a certain angle of incidence (called critical angle), the ray is completely reflected back into the denser medium. This is called total internal reflection.
For a spherical surface separating two media, the refraction relation is:
$
\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}
$
where $R=$ radius of curvature of the spherical surface.
A lens is a transparent medium bounded by two spherical surfaces.
The lens maker's formula is:
$
\frac{1}{f}=(n-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)
$
where $f=$ focal length, $n=$ refractive index, $R_1, R_2=$ radii of curvature.
Power is the ability of a lens to converge or diverge light.
$
P=\frac{100}{f(\text { in } \mathrm{cm})}=\frac{1}{f(\text { in } \mathrm{m})}
$
Unit: Dioptre (D)
If two or more thin lenses of focal lengths $f_1, f_2, f_3 \ldots$ are placed in contact, their effective focal length is:
$
\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}+\frac{1}{f_3}+\ldots
$
When light passes through a prism, it gets deviated.
Angle of deviation:
$
\delta=\left(i_1+i_2\right)-A
$
At the angle of minimum deviation:
$
n=\frac{\sin \left(\frac{A+\delta_m}{2}\right)}{\sin \left(\frac{A}{2}\right)}
$
where $A=$ angle of prism, $\delta_m=$ minimum deviation.
Total magnification:
$
M=M_o \times M_e
$
Magnifying power:
$
M=\frac{f_o}{f_e}
$
where $f_o=$ focal length of objective, $f_e=$ focal length of eyepiece.
Physics ray optics, a branch of optics, focuses on the behaviour of light as it travels in straight lines or rays. It explains the formation of images by mirrors (concave and convex) and lenses (convex and concave). Optical instruments, such as microscopes and telescopes, rely on the principles of ray optics to magnify and enhance the observation of objects. Understanding ray optics is essential for designing and optimizing these instruments. It also plays a crucial role in correcting vision problems through eyeglasses, which utilize lenses based on the principles of ray optics.
Formulas for Ray Optics and Optical Instruments
1. Mirror Formula
$
\frac{1}{f}=\frac{1}{v}+\frac{1}{u}
$
Magnification (Mirror):
$
M=\frac{h^{\prime}}{h}=\frac{v}{u}
$
where $h^{\prime}=$ image height, $h=$ object height
2. Refraction (Snell's Law)
$
n_1 \sin i=n_2 \sin r
$
3. Refraction at Spherical Surface
$
\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}
$
4. Lens Formula
$
\frac{1}{f}=\frac{1}{v}-\frac{1}{u}
$
Magnification (Lens):
$
M=\frac{h^{\prime}}{h}=\frac{v}{u}
$
5. Power of a Lens
$
P=\frac{100}{f(\text { in } \mathrm{cm})}=\frac{1}{f(\text { in } \mathrm{m})}
$
Unit: Dioptre (D)
6. Combination of Lenses in Contact
$
\frac{1}{f_{e q}}=\frac{1}{f_1}+\frac{1}{f_2}+\frac{1}{f_3}+\ldots
$
7. Prism Formula
$
\mu=\frac{\sin \left(\frac{A+D_m}{2}\right)}{\sin \left(\frac{A}{2}\right)}
$
8. Microscope
Magnifying Power (Simple Microscope):
$
M=1+\frac{D}{f}
$
Compound Microscope:
$
M=\left(\frac{L}{f_o}\right)\left(1+\frac{D}{f_e}\right)
$
where $f_o=$ focal length of objective, $f_e=$ focal length of eyepiece, $L=$ length of tube
9. Telescope
Magnifying Power (Normal Adjustment):
$
M=\frac{f_o}{f_e}
$
Telescope with Final Image at Least Distance of Distinct Vision:
$
M=\left(\frac{f_o}{f_e}\right)\left(1+\frac{f_e}{D}\right)
$
Also Check,
Mirrors – Convex mirrors in vehicles, concave mirrors in shaving/makeup.
Lenses – Spectacles, contact lenses, magnifying glass.
Prisms – Used in periscopes, binoculars, and spectrometers.
Optical Instruments – Microscope for tiny objects, telescope for distant objects, camera for images.
Human Eye – Natural convex lens forms real images on the retina.
Exam | Approximate Weightage | Remarks |
---|---|---|
NEET | 1-2 Question | Image formation, lens formula, and optical instruments are frequently asked. |
Board | 10 Marks | Important for derivations (mirror/lens formula, prism, optical instruments) and numericals. |
JEE | 1-2 Question | Conceptual + numerical questions, especially lens/mirror combinations, optical instruments, and prism deviations. |
To build a strong conceptual foundation, begin by referring to the NCERT book for both theory and practice questions. This comprehensive resource will help you understand the fundamental concepts of class 12 ray optics and optical instruments. After completing the NCERT book, you can further enhance your problem-solving skills by solving questions from the NCERT Exemplar book. For more advanced-level questions, you can explore additional reference books like "Concepts of Physics" by H.C. Verma or "Understanding Physics" by DC Pandey. These books provide a deeper understanding of the subject and offer challenging problems to test your knowledge.
Chapters No. | Chapters Name |
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Chapter 1 | |
Chapter 2 | |
Chapter 3 | |
Chapter 4 | |
Chapter 5 | |
Chapter 6 | |
Chapter 7 | |
Chapter 8 | |
Chapter 9 | |
Chapter 10 | |
Chapter 11 | |
Chapter 12 | |
Chapter 13 | |
Chapter 14 | |
Chapter 15 | |
Chapter 17 | |
Chapter 18 | |
Chapter 19 | |
Chapter 20 | |
Chapter 21 |
Frequently Asked Questions (FAQs)
Concave mirrors curve inward and can create both real and virtual images, while convex mirrors curve outward and only produce virtual images.
A converging lens is thicker in the middle and can form both real and virtual images, while a diverging lens is thinner in the middle and only produces virtual images.
The focal length of a lens is the distance between the lens and its focal point, where parallel rays of light converge or appear to converge after passing through the lens.
Total internal reflection occurs when light travelling from a denser medium to a less dense medium strikes the boundary at an angle greater than the critical angle. This causes the light to be completely reflected back into the denser medium instead of being refracted