Question

For the combination of one prism and 2 lenses shown in figure, find the size of the final image (in mm) when the object, length 1 cm, is located as shown in the figure. Refractive index of material from which prism is made is µ = 1.5.

Answer 1

48 mm

Answer 2

Solution Explanation:

1. Converging Lens (f₁ = 20 cm):

 • Use the Cartesian sign convention (object on left has u negative).
 • The object (after the prism, whose deviation does not affect the size) is 10 cm from the converging lens so u₁ = –10 cm.
 • Lens‐formula:
   1/v₁ = 1/f₁ – 1/u₁ = 1/20 – (–1/10) = 1/20 + 1/10 = 3/20
   ⇒ v₁ = 20/3 cm ≈ 6.67 cm (real image, to the right).
 • Magnification: m₁ = v₁/u₁ = (20/3)/(–10) = –2/3.
   Thus the image height from this lens is: 6 cm × (2/3) = 4 cm (the minus indicates inversion).

2. Diverging Lens (f₂ = –10 cm):

 • The diverging lens is 5 cm to the right of the converging lens.
 • The image from the first lens is 20/3 cm (≈6.67 cm) to the right of the converging lens so its position relative to the diverging lens is:    u₂ (for diverging lens) = –[v₁ – 5] = –(20/3 – 5) = –(20–15)/3 = –5/3 cm.  • Apply the lens formula for the diverging lens:    1/v₂ = 1/f₂ – 1/u₂ = 1/(–10) – 1/(–5/3)       = –0.1 + (3/5) = 0.5  ⇒ v₂ = 2 cm.  • Its magnification: m₂ = v₂/u₂ = 2/(–5/3) = –6/5.

3. Overall Magnification and Final Image Size:

 • Total magnification m = m₁ × m₂ = (–2/3) × (–6/5) = 12/15 = 4/5 = 0.8.
 • Therefore, the final image height = 6 cm × 0.8 = 4.8 cm = 48 mm.

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Answer: The final image is 48 mm in size.

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