🔢 The Human Eye and the Colourful World

Class 10 Science • Chapter 11
Important Numericals • Vision Correction • Lens Power

📘 Numerical Practice

इस chapter में numerical questions मुख्य रूप से vision defects, corrective lenses, focal length, lens power और near/far point से जुड़े होते हैं। पहले question को खुद solve करें।

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📐 Important Formulae

Power of Lens P = 1/f

Focal Length f = 1/P

Lens Formula 1/f = 1/v - 1/u

Lens Magnification m = v/u

Refractive Index n = c/v

Speed in Medium v = c/n

20 TOTAL NUMERICALS

4 EASY

8 HARD + VERY HARD

4 EXPERT

Numerical 1 – Lens Power

EASY

Lens Power

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

आसान भाषा में: Focal length 50 cm दी गई है। Power निकालने के लिए पहले centimetre को metre में बदलेंगे, फिर P = 1/f लगाएंगे।

✅ Step-by-Step Solution

f = 50 cm = 0.50 m

P = 1/f

P = 1/0.50 = +2 D

Final Answer: +2 D

Numerical 2 – Focal Length from Power

EASY

Lens Power

A corrective lens has a power of +4 D. Find its focal length.

आसान भाषा में: Power दी गई है। Focal length निकालने के लिए f = 1/P formula लगाएँगे।

✅ Step-by-Step Solution

P = +4 D

f = 1/P

f = 1/4 = 0.25 m

Final Answer: f = +0.25 m = +25 cm

Numerical 3 – Concave Lens

EASY

Lens • Myopia

A concave corrective lens has a focal length of -50 cm. Find its power.

आसान भाषा में: Concave lens की focal length negative है। 50 cm को -0.50 m में बदलकर P = 1/f लगाएंगे।

✅ Step-by-Step Solution

f = -50 cm = -0.50 m

P = 1/f

P = 1/(-0.50) = -2 D

Final Answer: -2 D

Numerical 4 – Negative Power

EASY

Lens • Corrective Lens

A person is prescribed a corrective lens of power -5 D. Find the focal length of the lens.

आसान भाषा में: Negative power का मतलब diverging corrective lens है। Focal length निकालने के लिए f = 1/P करेंगे।

✅ Step-by-Step Solution

P = -5 D

f = 1/P

f = 1/(-5) = -0.20 m

Final Answer: f = -0.20 m = -20 cm

Numerical 5 – Myopia Correction

MODERATE

Myopia • Corrective Lens

A myopic person can see clearly only up to 2 m. Find the power of the concave lens required to see distant objects clearly.

आसान भाषा में: व्यक्ति का far point 2 m है। Distant object को infinity पर माना जाएगा। Corrective concave lens ऐसा virtual image बनाएगा जो व्यक्ति के far point पर हो।

✅ Step-by-Step Solution

Object distance, u = -∞

Image distance, v = -2 m

Lens formula: 1/f = 1/v - 1/u

1/f = -1/2 - 0

f = -2 m

P = 1/f = -1/2 D

Final Answer: P = -0.5 D

Numerical 6 – Myopia with Far Point

MODERATE

Myopia • Power

A student's far point is 1.5 m. Calculate the focal length and power of the concave lens needed to correct the myopia for distant vision.

आसान भाषा में: Far point 1.5 m है। Infinity पर रखे distant object की image corrective lens द्वारा far point पर बननी चाहिए।

✅ Step-by-Step Solution

u = -∞

v = -1.5 m

1/f = 1/v - 1/u

1/f = -1/1.5

f = -1.5 m

P = 1/(-1.5) ≈ -0.67 D

Final Answer: f = -1.5 m, P ≈ -0.67 D

Numerical 7 – Hypermetropia Correction

MODERATE

Hypermetropia • Corrective Lens

A hypermetropic person has a near point of 100 cm. Find the power of the convex lens required so that the person can read a book at 25 cm.

आसान भाषा में: व्यक्ति की आँख 100 cm तक ही पास की वस्तु clearly देख सकती है। उसे 25 cm पर रखी book की virtual image 100 cm पर चाहिए। इसलिए convex lens का उपयोग होगा।

✅ Step-by-Step Solution

Object distance, u = -25 cm

Virtual image distance, v = -100 cm

1/f = 1/v - 1/u

1/f = -1/100 + 1/25

1/f = 3/100

f = 33.33 cm = 0.3333 m

P ≈ +3 D

Final Answer: P ≈ +3 D

Numerical 8 – Hypermetropia Focal Length

MODERATE

Hypermetropia • Focal Length

A person's near point is 50 cm. A book is held at 25 cm from the eye. Find the focal length of the corrective lens.

आसान भाषा में: आँख की near point 50 cm है। 25 cm की book की virtual image corrective lens के कारण 50 cm पर बननी चाहिए।

✅ Step-by-Step Solution

u = -25 cm

v = -50 cm

1/f = 1/v - 1/u

1/f = -1/50 + 1/25 = 1/50

f = +50 cm = +0.50 m

Final Answer: f = +50 cm

Numerical 9 – Hypermetropia Power

HARD

Hypermetropia • Power

A person has a near point of 75 cm. Calculate the power of the corrective convex lens required to read at 25 cm.

आसान भाषा में: 25 cm की वस्तु की image 75 cm के near point पर virtual बनानी है। Lens formula से f निकालकर फिर power निकालेंगे।

✅ Step-by-Step Solution

u = -25 cm

v = -75 cm

1/f = 1/v - 1/u

1/f = -1/75 + 1/25

1/f = 2/75

f = 37.5 cm = 0.375 m

P = 1/0.375 ≈ +2.67 D

Final Answer: P ≈ +2.67 D

Numerical 10 – Lens Power Comparison

HARD

Lens • Power

Two corrective lenses have powers +2 D and -3 D. Find their focal lengths and identify which lens is converging and which is diverging.

आसान भाषा में: दोनों lenses की power दी गई है। f = 1/P से दोनों focal lengths निकालें। Positive power converging lens और negative power diverging lens को दर्शाती है।

✅ Step-by-Step Solution

For P₁ = +2 D: f₁ = 1/2 = +0.50 m

For P₂ = -3 D: f₂ = 1/(-3) = -0.333 m

Final Answer: +2 D → f = +0.50 m, convex
-3 D → f ≈ -0.333 m, concave

Numerical 11 – Myopia and Lens Formula

HARD

Myopia • Lens Formula

A myopic person has a far point of 80 cm. Find the focal length and power of the lens required for distant vision.

आसान भाषा में: Distant object infinity पर है और corrective concave lens उसकी virtual image far point यानी 80 cm पर बनाएगी।

✅ Step-by-Step Solution

u = -∞

v = -80 cm = -0.80 m

1/f = 1/v - 1/u

1/f = -1/0.80

f = -0.80 m

P = 1/(-0.80) = -1.25 D

Final Answer: f = -0.80 m, P = -1.25 D

Numerical 12 – Hypermetropia Power

HARD

Hypermetropia • Lens Power

A person's near point is 80 cm. What power of convex lens is required to enable the person to read an object at 40 cm?

आसान भाषा में: Book 40 cm पर है और आँख की near point 80 cm है। Corrective convex lens को 40 cm की book की virtual image 80 cm पर बनानी होगी।

✅ Step-by-Step Solution

u = -40 cm

v = -80 cm

1/f = -1/80 + 1/40

1/f = 1/80

f = 80 cm = 0.80 m

P = 1/0.80 = +1.25 D

Final Answer: P = +1.25 D

Numerical 13 – Myopia Correction at Infinity

VERY HARD

Myopia • Application

A student's far point is 50 cm. A distant tree is considered to be at infinity. Calculate the focal length and power of the concave corrective lens.

आसान भाषा में: Infinity पर object के लिए u = -∞ होगा। Corrective lens distant object की virtual image far point यानी 50 cm पर बनाएगा।

✅ Step-by-Step Solution

u = -∞

v = -50 cm = -0.50 m

1/f = 1/v = -1/0.50

f = -0.50 m

P = -2 D

Final Answer: f = -0.50 m, P = -2 D

Numerical 14 – Hypermetropia with Near Point

VERY HARD

Hypermetropia • Application

A person has a near point of 100 cm. Find the power of the convex lens required to read a book at 50 cm.

आसान भाषा में: Book को 50 cm पर रखा गया है लेकिन व्यक्ति केवल 100 cm तक की near object को clear देख सकता है। इसलिए lens को book की virtual image 100 cm पर बनानी होगी।

✅ Step-by-Step Solution

u = -50 cm

v = -100 cm

1/f = -1/100 + 1/50

1/f = 1/100

f = 100 cm = 1 m

P = +1 D

Final Answer: P = +1 D

Numerical 15 – Lens Power and Focal Length

VERY HARD

Corrective Lens • Power

A corrective lens has power -2.5 D. Calculate its focal length in centimetres and identify the type of lens.

आसान भाषा में: Power negative है, इसलिए lens concave/diverging होगा। पहले f = 1/P निकालें और फिर metre को centimetre में बदलें।

✅ Step-by-Step Solution

P = -2.5 D

f = 1/P

f = 1/(-2.5) = -0.40 m

-0.40 m = -40 cm

Final Answer: f = -40 cm; Concave lens

Numerical 16 – Combined Lens Power

VERY HARD

Lens • Combined Power

Two thin lenses of powers +2 D and -1 D are placed in contact. Find the combined power and focal length of the combination.

आसान भाषा में: जब दो thin lenses contact में हों, तो उनकी powers algebraically add होती हैं। पहले combined power निकालें, फिर f = 1/P से focal length निकालें।

✅ Step-by-Step Solution

P = P₁ + P₂

P = +2 + (-1) = +1 D

f = 1/P = 1/1 = +1 m

Final Answer: Combined Power = +1 D, Focal Length = +1 m

Numerical 17 – Myopia Expert Challenge

EXPERT

Myopia • Multi-Step

A myopic student has a far point of 2.5 m. Determine the power of the corrective lens. Also state whether the lens is converging or diverging.

आसान भाषा में: Far point 2.5 m है। Distant object infinity पर माना जाएगा। Corrective lens virtual image far point पर बनाएगा, इसलिए lens concave होगी।

✅ Step-by-Step Solution

u = -∞

v = -2.5 m

1/f = -1/2.5

f = -2.5 m

P = 1/(-2.5) = -0.4 D

Final Answer: P = -0.4 D; Diverging (concave) lens

Numerical 18 – Hypermetropia Expert Challenge

EXPERT

Hypermetropia • Multi-Step

A person has a near point of 1 m. Find the power of the corrective lens required to read a book placed at 25 cm from the eye.

आसान भाषा में: Normal reading distance 25 cm है। लेकिन व्यक्ति की near point 100 cm है। इसलिए 25 cm की object की virtual image 100 cm पर बनानी होगी।

✅ Step-by-Step Solution

u = -25 cm = -0.25 m

v = -100 cm = -1 m

1/f = 1/v - 1/u

1/f = -1 + 4 = 3 m⁻¹

f = 1/3 m

P = +3 D

Final Answer: P = +3 D

Numerical 19 – Corrective Lens Identification

EXPERT

Vision Defect • Application

A person is prescribed a lens of focal length -80 cm. Calculate its power and identify the likely type of corrective lens. What vision defect is commonly corrected using such a lens?

आसान भाषा में: Focal length negative है। इसलिए power negative होगी और lens concave होगी। ऐसी lens commonly myopia correction में उपयोग होती है।

✅ Step-by-Step Solution

f = -80 cm = -0.80 m

P = 1/f

P = 1/(-0.80) = -1.25 D

Negative power → diverging / concave lens

Final Answer: P = -1.25 D; Concave lens; commonly used for myopia

Numerical 20 – Final Expert Problem

EXPERT

Vision Correction • Mixed

A person has a near point of 75 cm. A corrective convex lens is placed in front of the eye so that an object at 25 cm can be seen clearly. Find the focal length and power of the lens. Also explain whether the image formed by the corrective lens should be real or virtual.

आसान भाषा में: व्यक्ति की near point 75 cm है। इसलिए 25 cm पर रखी वस्तु की image lens को 75 cm पर बनानी होगी ताकि eye उसे clearly देख सके। Corrective convex lens के लिए यह image virtual होगी।

✅ Step-by-Step Solution

Object distance: u = -25 cm

Required virtual image: v = -75 cm

1/f = 1/v - 1/u

1/f = -1/75 + 1/25

1/f = 2/75

f = 37.5 cm

f = 0.375 m

P = 1/0.375 ≈ +2.67 D

Since v is negative, the corrective lens forms a virtual image on the same side as the object.

Final Answer: f = +37.5 cm, P ≈ +2.67 D, Virtual Image

🔎 इस difficulty में कोई numerical उपलब्ध नहीं है।