🔢 Light – Reflection and Refraction

Class 10 Science • Chapter 10
Important Numericals • Formulae • Step-by-Step Solutions

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📘 Numerical Practice

इस chapter के numerical questions को Easy से Expert level तक arrange किया गया है। पहले question को खुद solve करें और उसके बाद आवश्यकता होने पर हिंदी में समझें या Solution देखें button का उपयोग करें।

🎯 Practice Mode: पहले खुद सवाल solve करने की कोशिश करें। अगर सवाल समझ में नहीं आ रहा है तो हिंदी में समझें दबाएँ। पूरा formula और calculation देखने के लिए Solution देखें दबाएँ।

📐 Important Formulae

Mirror Formula 1/f = 1/v + 1/u
Mirror Magnification m = -v/u
Radius of Curvature R = 2f
Lens Formula 1/f = 1/v - 1/u
Lens Power P = 1/f
Refractive Index n = c/v
Speed in Medium v = c/n
Lens Magnification m = v/u
🎯 Difficulty Filter
20 TOTAL NUMERICALS
4 EASY
8 HARD + VERY HARD
4 EXPERT
Numerical 1 – Focal Length
EASY
Mirror • Focal Length

A concave mirror has a radius of curvature of 30 cm. Find its focal length.

आसान भाषा में: सवाल में radius of curvature दी गई है। हमें focal length निकालनी है। Spherical mirror में radius focal length की दो गुनी होती है, इसलिए radius को 2 से divide करेंगे।
✅ Step-by-Step Solution
Given: R = 30 cm
Formula: R = 2f
f = R/2
f = 30/2 = 15 cm
Final Answer: 15 cm
Numerical 2 – Radius of Curvature
EASY
Mirror • Radius

A spherical mirror has a focal length of 12 cm. Find its radius of curvature.

आसान भाषा में: Focal length दी हुई है। Radius of curvature निकालने के लिए R = 2f formula लगाएंगे।
✅ Step-by-Step Solution
Given: f = 12 cm
Formula: R = 2f
R = 2 × 12 = 24 cm
Final Answer: 24 cm
Numerical 3 – Refractive Index
EASY
Refraction • Refractive Index

The speed of light in a medium is 2 × 10⁸ m/s. If the speed of light in vacuum is 3 × 10⁸ m/s, find the refractive index.

आसान भाषा में: Vacuum में light की speed और medium में light की speed दी गई है। दोनों का ratio लेकर refractive index निकालेंगे।
✅ Step-by-Step Solution
Given: c = 3 × 10⁸ m/s
v = 2 × 10⁸ m/s
Formula: n = c/v
n = 3/2 = 1.5
Final Answer: n = 1.5
Numerical 4 – Lens Power
EASY
Lens • Power

A convex lens has a focal length of 50 cm. Find its power.

आसान भाषा में: Power निकालने के लिए focal length को metre में convert करके P = 1/f formula लगाएंगे।
✅ Step-by-Step Solution
Given: f = 50 cm = 0.50 m
Formula: P = 1/f
P = 1/0.50 = +2 D
Final Answer: +2 D
Numerical 5 – Mirror Formula
MODERATE
Concave Mirror • Mirror Formula

An object is placed 30 cm in front of a concave mirror having focal length 15 cm. Find the position of the image.

आसान भाषा में: Concave mirror के लिए focal length और object distance दोनों negative होंगे। फिर mirror formula लगाकर image distance निकालेंगे।
✅ Step-by-Step Solution
Given: u = -30 cm, f = -15 cm
Formula: 1/f = 1/v + 1/u
-1/15 = 1/v - 1/30
1/v = -1/30
v = -30 cm
Final Answer: v = -30 cm
Numerical 6 – Mirror Magnification
MODERATE
Mirror • Magnification

A concave mirror forms an image at 20 cm when the object is placed at 40 cm. Find the magnification.

आसान भाषा में: Image distance और object distance दोनों use होंगे। Mirror magnification formula m = -v/u लगाया जाएगा।
✅ Step-by-Step Solution
Given: u = -40 cm, v = -20 cm
Formula: m = -v/u
m = -(-20)/(-40)
m = -0.5
Final Answer: m = -0.5
Numerical 7 – Concave Lens Power
MODERATE
Lens • Power

A concave lens has a focal length of -25 cm. Find its power.

आसान भाषा में: Concave lens की focal length negative होती है। पहले cm को metre में बदलकर power निकालेंगे।
✅ Step-by-Step Solution
Given: f = -25 cm = -0.25 m
Formula: P = 1/f
P = 1/(-0.25) = -4 D
Final Answer: -4 D
Numerical 8 – Speed of Light
MODERATE
Refraction • Speed

The refractive index of a transparent medium is 1.5. Calculate the speed of light in the medium if c = 3 × 10⁸ m/s.

आसान भाषा में: Refractive index और vacuum में speed दी है। Medium में speed निकालने के लिए c को n से divide करेंगे।
✅ Step-by-Step Solution
Given: n = 1.5
c = 3 × 10⁸ m/s
Formula: v = c/n
v = (3 × 10⁸)/1.5
Final Answer: v = 2 × 10⁸ m/s
Numerical 9 – Concave Mirror Image
HARD
Mirror • Image Formation

An object is placed 24 cm in front of a concave mirror having a focal length of 18 cm. Find the image distance.

आसान भाषा में: Object distance और concave mirror की focal length negative लेकर mirror formula लगाएंगे।
✅ Step-by-Step Solution
u = -24 cm
f = -18 cm
1/f = 1/v + 1/u
-1/18 = 1/v - 1/24
1/v = -1/72
Final Answer: v = -72 cm
Numerical 10 – Convex Lens Image
HARD
Lens • Lens Formula

An object is placed 30 cm in front of a convex lens having a focal length of 20 cm. Find the image distance.

आसान भाषा में: Convex lens की focal length positive और object distance negative होगा। Lens formula लगाकर image distance निकालेंगे।
✅ Step-by-Step Solution
u = -30 cm
f = +20 cm
1/f = 1/v - 1/u
1/20 = 1/v + 1/30
1/v = 1/60
Final Answer: v = +60 cm
Numerical 11 – Lens Magnification
HARD
Lens • Magnification

A convex lens forms an image at 60 cm when the object is placed at 30 cm. Find the magnification.

आसान भाषा में: Lens magnification के लिए image distance को object distance से divide करेंगे और sign convention का ध्यान रखेंगे।
✅ Step-by-Step Solution
u = -30 cm
v = +60 cm
Formula: m = v/u
m = 60/(-30) = -2
Final Answer: m = -2
Numerical 12 – Power Difference
HARD
Lens • Power Comparison

Two convex lenses have focal lengths of 20 cm and 40 cm. Find the difference between their powers.

आसान भाषा में: दोनों focal lengths को metre में बदलें। दोनों lens की power निकालकर उनका difference लें।
✅ Step-by-Step Solution
f₁ = 20 cm = 0.20 m
P₁ = 1/0.20 = +5 D
f₂ = 40 cm = 0.40 m
P₂ = 1/0.40 = +2.5 D
Difference = 5 - 2.5 = 2.5 D
Final Answer: 2.5 D
Numerical 13 – Refractive Index Ratio
HARD
Refraction • Ratio

The speed of light in medium A is 2.0 × 10⁸ m/s and in medium B is 2.5 × 10⁸ m/s. Find the ratio of their refractive indices.

आसान भाषा में: Refractive index n = c/v है। Ratio निकालते समय c cancel हो जाएगा, इसलिए speed का उल्टा ratio लेना होगा।
✅ Step-by-Step Solution
nA = c/vA
nB = c/vB
nA/nB = vB/vA
= 2.5/2.0 = 1.25
Final Answer: nA : nB = 1.25 : 1
Numerical 14 – Lens Image Distance
HARD
Convex Lens • Application

A convex lens has a focal length of 15 cm and an object is placed 25 cm in front of it. Find the image distance.

आसान भाषा में: Convex lens के लिए f positive होगा और object distance negative होगा। Lens formula लगाएँ।
✅ Step-by-Step Solution
u = -25 cm
f = +15 cm
1/15 = 1/v + 1/25
1/v = 1/15 - 1/25 = 2/75
v = 75/2 = 37.5 cm
Final Answer: v = +37.5 cm
Numerical 15 – Speed Reduction
HARD
Refraction • Speed

The refractive index of glass is 1.5. If the speed of light in vacuum is 3 × 10⁸ m/s, calculate the reduction in speed of light in glass.

आसान भाषा में: पहले glass में light की speed निकालेंगे। फिर vacuum की speed में से glass की speed घटाएँगे।
✅ Step-by-Step Solution
n = 1.5
c = 3 × 10⁸ m/s
v = c/n
v = (3 × 10⁸)/1.5 = 2 × 10⁸ m/s
Reduction = 3 × 10⁸ - 2 × 10⁸
Final Answer: 1 × 10⁸ m/s
Numerical 16 – Mirror + Magnification
VERY HARD
Concave Mirror • Mixed

A concave mirror has a focal length of 20 cm. An object is placed 30 cm in front of it. Find the image distance and magnification.

आसान भाषा में: यह दो-step question है। पहले mirror formula से image distance निकालें। फिर उसी u और v से magnification निकालें।
✅ Step-by-Step Solution
u = -30 cm
f = -20 cm
-1/20 = 1/v - 1/30
1/v = -1/60
v = -60 cm
m = -v/u
m = -(-60)/(-30) = -2
Final Answer: v = -60 cm, m = -2
Numerical 17 – Lens Formula + Power
VERY HARD
Lens • Formula + Power

A convex lens forms a real image at 50 cm when the object is placed 25 cm in front of it. Find its focal length and power.

आसान भाषा में: पहले lens formula से focal length निकालेंगे। फिर उसे metre में बदलकर power निकालेंगे।
✅ Step-by-Step Solution
u = -25 cm
v = +50 cm
1/f = 1/v - 1/u
1/f = 1/50 + 1/25 = 3/50
f = 50/3 ≈ 16.67 cm
f ≈ 0.1667 m
P = 1/0.1667 ≈ +6 D
Final Answer: f ≈ +16.67 cm, P ≈ +6 D
Numerical 18 – Refractive Index Challenge
VERY HARD
Refraction • Calculation

A transparent material allows light to travel at 2.4 × 10⁸ m/s. Calculate its refractive index if the speed of light in vacuum is 3 × 10⁸ m/s.

आसान भाषा में: Medium में light की speed और vacuum की speed दी हुई है। n = c/v से refractive index निकालना है।
✅ Step-by-Step Solution
c = 3 × 10⁸ m/s
v = 2.4 × 10⁸ m/s
n = c/v
n = 3/2.4 = 1.25
Final Answer: n = 1.25
Numerical 19 – Expert Mirror Problem
EXPERT
Concave Mirror • Expert

A concave mirror forms a real image three times the size of an object. If its focal length is 18 cm, find the object distance and image distance.

आसान भाषा में: Real image inverted होती है, इसलिए magnification -3 होगा। पहले magnification से v और u का relation बनाएँगे और फिर mirror formula लगाएंगे।
✅ Step-by-Step Solution
m = -3
m = -v/u
-3 = -v/u → v = 3u
f = -18 cm
-1/18 = 1/(3u) + 1/u
-1/18 = 4/(3u)
u = -24 cm
v = 3u = -72 cm
Final Answer: u = -24 cm, v = -72 cm
Numerical 20 – Expert Lens Problem
EXPERT
Convex Lens • Expert

A convex lens produces a real image twice the size of the object. The object is placed 15 cm from the lens. Find the image distance and focal length.

आसान भाषा में: Real image twice the size की है। इसलिए magnification -2 होगा। इससे पहले image distance निकालेंगे और फिर lens formula से focal length निकालेंगे।
✅ Step-by-Step Solution
u = -15 cm
m = -2
m = v/u
-2 = v/(-15)
v = +30 cm
1/f = 1/v - 1/u
1/f = 1/30 + 1/15 = 1/10
f = +10 cm
Final Answer: v = +30 cm, f = +10 cm
🔎 इस difficulty में कोई numerical उपलब्ध नहीं है।
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