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Geometrical Optics question

2025 · 8 Apr · Shift 2 · Q52
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  5. /2025 · 8 Apr · Shift 2 · Q52

Geometrical Optics question

2025 · 8 Apr · Shift 2 · Q52

JEE MainPhysicsGeometrical OpticsMCQ+4 / −1
A convex lens of focal length 30 cm is placed in contact with a concave lens of focal length 20 cm. An object is placed at 20 cm to the left of this lens system. The distance of the image from the lens in cm is ‾\underline{\hspace{2cm}}​.
  1. A
    607\frac{60}{7}760​
  2. B
    15
  3. C
    45
  4. D
    30
View written solutionFree

Correct answer: B

  1. Given data
  • Convex lens focal length: f1=+30 cmf_1 = +30\text{ cm}f1​=+30 cm
  • Concave lens focal length: f2=−20 cmf_2 = -20\text{ cm}f2​=−20 cm
  • The two lenses are in contact, so we first find the equivalent focal length.
  • Object distance from the lens system: u=−20 cmu = -20\text{ cm}u=−20 cm

(Using Cartesian sign convention: object on the left gives negative uuu.)

  1. Equivalent focal length of the combination

For thin lenses in contact,

1F=1f1+1f2\frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2}F1​=f1​1​+f2​1​

Substitute values:

1F=130+1−20=130−120\frac{1}{F} = \frac{1}{30} + \frac{1}{-20} = \frac{1}{30} - \frac{1}{20}F1​=301​+−201​=301​−201​

Taking LCM 606060,

1F=2−360=−160\frac{1}{F} = \frac{2 - 3}{60} = -\frac{1}{60}F1​=602−3​=−601​

So,

F=−60 cmF = -60\text{ cm}F=−60 cm

Thus the combination behaves like a concave lens of focal length −60-60−60 cm.

  1. Apply lens formula

Lens formula:

1v−1u=1f\frac{1}{v} - \frac{1}{u} = \frac{1}{f}v1​−u1​=f1​

Here,

u=−20 cm,f=−60 cmu = -20\text{ cm}, \quad f = -60\text{ cm}u=−20 cm,f=−60 cm

So,

1v−1−20=1−60\frac{1}{v} - \frac{1}{-20} = \frac{1}{-60}v1​−−201​=−601​

That is,

1v+120=−160\frac{1}{v} + \frac{1}{20} = -\frac{1}{60}v1​+201​=−601​

Therefore,

1v=−160−120\frac{1}{v} = -\frac{1}{60} - \frac{1}{20}v1​=−601​−201​ 1v=−160−360=−460=−115\frac{1}{v} = -\frac{1}{60} - \frac{3}{60} = -\frac{4}{60} = -\frac{1}{15}v1​=−601​−603​=−604​=−151​

Hence,

v=−15 cmv = -15\text{ cm}v=−15 cm
  1. Interpretation

The negative sign means the image is formed on the left side of the lens system (virtual image).

So the distance of the image from the lens is:

15 cm15\text{ cm}15 cm
  1. Option check
  • A: 607\frac{60}{7}760​ ❌
  • B: 151515 ✅
  • C: 454545 ❌
  • D: 303030 ❌

Therefore, the correct option is B.

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