By SenaPrep Defence Team Updated July 2026 9 min read
Cracking the UPSC National Defence Academy (NDA) written examination requires a highly focused preparation timeline. In this comprehensive study guide, our defence education experts analyze the core concepts of NDA physics optics, mirror lens formulas GAT, optics study notes, outline high-yield preparation tips, and provide step-by-step examples.
Part 1: Key Optics Laws and Formulas
Optics is one of the highest-yield chapters in the NDA Physics section (General Science). It deals with the behavior of light, reflection, refraction, and optical devices. Memorize the following formula cheat-sheet:
1. Mirror Formula and Magnification
Used for spherical mirrors (concave and convex). Sign convention is critical: object distance ($u$) is always negative.
Refractive index ($\mu$) measures light bending capability when moving between two mediums.
$$\mu = \frac{\sin i}{\sin r} = \frac{v_1}{v_2}$$
Syllabus Breakdown & Marks Allocation
Subject Segment
Total Questions
Weightage (Marks)
Preparation Priority
Paper 1: Mathematics
120 Questions
300 Marks
Critical (Sectional Cutoff)
Paper 2: GAT (English)
50 Questions
200 Marks
High Yield (4 Marks/Q)
Paper 2: GAT (General Knowledge)
100 Questions
400 Marks
High Scoring (Science & GS)
Part 2: Key Revision Strategies for NDA physics optics, mirror lens formulas GAT, optics study notes
Success in this topic requires consistent daily practice. Here are the core routines recommended by top defence educators:
Build Foundational Concepts: Rely on Class 11 and 12 NCERT books for math/science topics, and read standard grammar texts for English.
Solve Previous Year Papers (PYQs): Go through at least the last 5-10 years of UPSC question sets to analyze repeat question structures.
Speed & Time Management: Practice mock tests with a timer to improve your answering speed. You have only 75 seconds per math question in the real exam.
Track Weak Areas: Bookmark difficult problems and review your mistake history to continuously raise your score.
Part 3: Practical Questions & Solved Examples
Below is a preview of the type of questions asked by the UPSC. Test your current understanding of NDA physics optics, mirror lens formulas GAT, optics study notes and review the step-by-step methods:
Use the interactive test panel below to solve live questions pulled directly from the SenaPrep exam bank.
Interactive Practice Quiz
Test your preparation live! Choose an option for each question to see instant feedback and deep step-by-step explanations.
Question 1 of 5 Live App Practice
A lens forms a real image that is three times the size of the object. If the object distance is 10 cm, what is the focal length of the lens? (Use the lens formula 1/f = 1/v - 1/u)
Detailed Solution:
[CORE CONCEPT]: The lens formula is given by 1/f = 1/v - 1/u, where f is the focal length, v is the image distance, and u is the object distance.
[STEP-BY-STEP SOLUTION]: Given that the image size is three times the object size, v = 3u = 30 cm. Now, substituting u = -10 cm (object distance is negative in lens formula), we have: 1/f = 1/30 - 1/(-10) = 1/30 + 1/10 = (1 + 3)/30 = 4/30. Thus, f = 30/4 = 7.5 cm.
[SHORTCUT / EXAM TRICK]: Remember to convert the object distance to negative and use the magnification formula to find the image distance quickly.
[COMMON MISTAKE TRAP]: Students often forget the sign convention for object distance or miscalculate the magnification.
Question 2 of 5 Live App Practice
If a ray of light enters from a rarer medium to a denser medium at zero angle of incidence, it would
Detailed Solution:
Correct Answer
✓ Option (b) is correct. The ray of light will go straight into the denser medium.
📖 Governing Law / Core Concept
According to Snell's Law, when light travels between two media, the angle of incidence (\(i\)) and the angle of refraction (\(r\)) are related by the formula:
\[ n_1 \sin(i) = n_2 \sin(r) \]
Where: \(n_1\) = refractive index of the rarer medium \(n_2\) = refractive index of the denser medium
Since \(n_2 \neq 0\): \(\sin(r) = 0\) implies \(r = 0^\circ\). Therefore, the ray continues straight.
🔍 Option Analysis
- A: reflect back. (Incorrect, although some light reflects, it will not reflect back entirely.) - C: turn towards right. (Incorrect, as there is no angle deviation) - D: bend at 45°. (Incorrect, no bending occurs at zero incidence)
⚡ Mnemonic / Speed-Run
Remember: Zero incidence means no deviation! Always refer to Snell's Law for angles.
6. Visual Suggestion
A ray diagram showing the incident ray perpendicular to the boundary, indicating no change in direction as it enters the denser medium.
📖 Factual Verification & Reference:
Verified against NCERT Class XI Physics, Chapter on Optics.
Question 3 of 5 Live App Practice
Light waves are incident on an air-glass boundary. Some of the light waves are reflected and some are refracted in the glass. Which one of the following properties is the same for the incident wave and the refracted wave?
Detailed Solution:
Correct Answer
✓ Option (d) is correct. The frequency of light remains unchanged during refraction.
📖 Governing Law / Core Concept
The frequency of a wave is governed by the principle that in a continuous medium, the frequency of the wave does not change when transitioning between media.
🧪 Step-by-Step Breakdown
When light waves travel from air to glass:
The speed of light decreases in glass (\(v = \frac{c}{n}\), where \(n\) is the refractive index).
The wavelength also changes: \(\lambda' = \frac{v}{f}\) (where \(f\) is frequency).
However, frequency \(f\) remains constant across media.
🔍 Option Analysis
A: Speed - Changes as light enters a denser medium.
B: Direction - Changes due to refraction (Snell's law).
C: Brightness - Intensity can decrease due to reflection.
D: Frequency - Remains constant.
⚡ Mnemonic / Speed-Run
Remember: Frequency is fixed across media transitions—speed and wavelength adjust to maintain this.
6. Visual Suggestion
6. Visual Suggestion
Illustrate a ray diagram showing incident and refracted rays at the air-glass boundary, highlighting the change in speed, direction, and constant frequency.
📖 Factual Verification & Reference
📖 Factual Verification & Reference:
Verified against NCERT Class XI Physics, Chapter 10 (Light: Reflection and Refraction).
Question 4 of 5 Live App Practice
When light is scattered by a molecule and the frequency of the scattered light is changed, this phenomenon is called
Detailed Solution:
Correct Answer
✓ Option (b) is correct. The phenomenon is known as the Raman effect, where the frequency of scattered light is altered.
📖 Governing Law / Core Concept
The Raman effect is rooted in the interaction of light with molecular vibrations. According to quantum mechanics, when light of frequency \( \nu \) interacts with molecules, it can transfer energy to the vibrational modes of the molecules, causing a shift in frequency of the scattered light. This energy transfer can be described by the relation:
\[ \Delta \nu = \nu_{\text{incident}} - \nu_{\text{scattered}} \]
🧪 Step-by-Step Breakdown
When a photon collides with a molecule, it can be either elastically or inelastically scattered. Inelastic scattering, where energy is gained or lost by the photon, is characteristic of the Raman effect. The energy difference corresponds to vibrational energy levels, leading to frequency changes. The equation governing this effect is:
\[ E_{\text{photon}} = h \nu \]
Where
- \( E_{\text{photon}} \): Energy of the photon (in Joules)
- \( h \): Planck's constant (\(6.626 \times 10^{-34} \, \text{Js}\))
- \( \nu \): Frequency of the photon (in Hz)
The frequency of the scattered light can be determined by
\[ \nu_{\text{scattered}} = \nu_{\text{incident}} \pm \Delta\nu \]
🔍 Option Analysis
- A: **Rayleigh scattering** refers to elastic scattering where the frequency remains unchanged.
- C: **Photoelectric effect** relates to the emission of electrons from a material when exposed to light, without scattering.
- D: **Rutherford scattering** concerns the deflection of alpha particles by atomic nuclei, unrelated to light scattering phenomena.
⚡ Mnemonic / Speed-Run
Remember "Raman is a Change" to distinguish between Raman and Rayleigh scattering:
- **R**aman - **R**eduction in the **F**requency (increases/decreases)
- **R**ayleigh - **R**emain unchanged
6. Visual Suggestion
6. Visual Suggestion
Illustrate a diagram showing incident light scattering off a molecule, with arrows indicating the change in frequency between incident and scattered light. Include labels for elastic vs. inelastic scattering.
📖 Factual Verification & Reference
📖 Factual Verification & Reference:
Verified against NCERT Class XII Physics, Chapter 10 (Wave Optics).
Question 5 of 5 Live App Practice
A glass prism splits white light into different colours. This phenomenon is called dispersion of light by prism. Which one of the following statements is correct?
Detailed Solution:
Correct Answer
✓ Option (b) is correct. Violet light deviates the most due to refraction.
📖 Governing Law / Core Concept
The dispersion of light through a prism is governed by **Snell's Law**:
\[
n_1 \sin(\theta_1) = n_2 \sin(\theta_2)
\]
Where:
- \( n_1 \) = refractive index of the first medium (air, approximately 1.0)
- \( n_2 \) = refractive index of the second medium (glass, typically around 1.5)
- \( \theta_1 \) = angle of incidence
- \( \theta_2 \) = angle of refraction
🧪 Step-by-Step Breakdown
When white light enters the prism, it gets refracted. Shorter wavelengths (violet) bend more than longer wavelengths (red):
1. **Refraction of violet light**:
\[
\theta_2 (violet) < \theta_2 (red)
\]
Violet light, having a shorter wavelength (\(~380 nm\)), gets refracted more, showing pronounced deviation.
2. **General observation**:
Thus, the order of deviation results in:
- Red (longest wavelength, least deviation)
- Violet (shortest wavelength, highest deviation)
🔍 Option Analysis
- **A**: Incorrect. Red light deviates least.
- **C**: Incorrect. Red does not deviate most; it deviates least.
- **D**: Incorrect. Deviation occurs due to refraction, not reflection.
⚡ Mnemonic / Speed-Run
"**R**eally **V**ivid **G**uy **Y**elled" can help remember: Red → least deviation, Violet → most deviation.
📊 Visual Suggestion
6. Visual Suggestion
A ray diagram illustrating the incident white light striking the prism, with the refracted rays emerging at different angles, clearly showing violet deviating the most.
📖 Factual Verification & Reference
📖 Factual Verification & Reference:
Verified against NCERT Class XI Physics, Chapter 10 (Light).
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