Question

The photograph of a house occupies an area of 1.75 \(\text{cm}^2\) on a 35 mm slide. The slide is projected on to a screen, and the area of the house on the screen is 1.55 \(\text m^2\). What is the linear magnification of the projector-screen arrangement.

Answer 1

Given:

Area of the photograph on the slide,
A₁ = 1.75 cm²

Area of the image on the screen,
A₂ = 1.55 m²

Convert area on screen into cm²:

1 m² = 10⁴ cm²

A₂ = 1.55 × 10⁴ = 1.55 × 10⁴ cm²

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Step 1: Relation between area magnification and linear magnification

Area magnification = (Linear magnification)²

Let linear magnification = m

m² = A₂ / A₁

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Step 2: Substitute given values

m² = (1.55 × 10⁴) / 1.75

m² ≈ 8.86 × 10³

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Step 3: Calculate linear magnification

m = √(8.86 × 10³)

m ≈ 94

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Final Answer:

The linear magnification of the projector–screen arrangement is approximately
94.