Refraction at Curved Surfaces, Lens, Power of Lens Quiz1

📘 WORKSHEET: Refraction at Curved Surfaces & Lenses

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🧠 SECTION A: THEORY / CONCEPTUAL (10 Questions)

Q1. Define refractive index. What does it signify physically?

Q2. State the sign convention used for spherical lenses.

Q3. What is the difference between a real image and a virtual image?

Q4. Define focal length of a lens.

Q5. What is power of a lens? Write its SI unit.

Q6. What happens to the focal length when the refractive index of lens material increases?

Q7. Why does a convex lens converge light rays?

Q8. What is the relation between radius of curvature and focal length for a thin lens?

Q9. Define magnification in case of a lens.

Q10. Can a concave lens form a real image? Justify your answer.

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🔢 SECTION B: NUMERICALS (10 Questions)

Use standard sign convention.

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Q11. An object is placed 20 cm in front of a convex lens of focal length 10 cm. Find image distance.

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Q12. A concave lens has focal length 15 cm. Find its power.

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Q13. An object is placed at 30 cm from a convex lens (f = 15 cm). Find magnification.

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Q14. Find the focal length of a lens of power +2 D.

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Q15. An image is formed at 40 cm by a convex lens when object is at 20 cm. Find focal length.

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Q16. A lens has focal length -25 cm. Identify type and find its power.

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Q17. Object at infinity forms image at 25 cm. Identify lens and find focal length.

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Q18. An object of height 2 cm forms image of height 6 cm. Find magnification.

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Q19. A convex lens produces an image at same distance as object. Find object distance in terms of focal length.

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Q20. Two lenses of powers +2 D and +3 D are combined. Find net power.

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✅ ANSWER KEY

Theory

1. Ratio of speed of light in vacuum to medium
2. Cartesian sign convention
3. Real: formed by actual rays; Virtual: apparent intersection
4. Distance between optical centre and focus
5. $P = 1/f$, unit: Dioptre (D)
6. Focal length decreases
7. Refraction bends rays toward principal axis
8. Depends on lens maker formula
9. $m = h_i/h_o = v/u$
   
10. No, always virtual

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Numericals

11. +20 cm
12. -6.67 D
13. -1
14. 0.5 m
15. 13.33 cm
16. Concave, -4 D
17. Convex, 25 cm
18. +3
19. $2f$
    
20. +5 D

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🧮 KEY FORMULA (IMPORTANT)

$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$

$u$

$f$

$\frac{1}{f}=\frac{1}{u}+\frac{1}{v},\ v\approx28,\ m\approx-1$

Also:

• $P = 1/f$(f in meters)
• $m = v/u$
  

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✍️ DETAILED SOLUTIONS

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Q11

$$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$$ $$\frac{1}{10} = \frac{1}{v} + \frac{1}{(-20)}$$$$\frac{1}{v} = \frac{1}{10} + \frac{1}{20} = \frac{3}{20}$$ $$v = 20 \, \text{cm}$$

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Q12

$$P = \frac{1}{f} = \frac{1}{-0.15} = -6.67 D$$

Q13

$$\frac{1}{15} = \frac{1}{v} + \frac{1}{(-30)} \Rightarrow \frac{1}{v} = \frac{1}{15} + \frac{1}{30} = \frac{1}{10}$$$$v = 10 \Rightarrow m = \frac{10}{-30} = -1$$

Q14

$$f = \frac{1}{P} = \frac{1}{2} = 0.5 \, m$$

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Q15

$$\frac{1}{f} = \frac{1}{40} + \frac{1}{(-20)} = \frac{1 - 2}{40} = -\frac{1}{40} \Rightarrow f = 13.33 \, cm$$

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Q16

$$P = \frac{1}{-0.25} = -4 D$$

Q17

Object at infinity → image at focus

$$f = 25 \, cm$$

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Q18

$$m = \frac{h_i}{h_o} = \frac{6}{2} = 3$$

Q19

For same distance:

$$u = v = 2f$$

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Q20

$$P_{total} = P_1 + P_2 = 2 + 3 = 5D$$