The photograph of a house occupies an area of 1.75 cm2 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 m2. What is the linear magnification of the projector-screen arrangement?

The photograph of a house occupies an area of 1.75 cm² 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 m². What is the linear magnification of the projector-screen arrangement?

Solution:

Given that

Area of the house on the slide = 1.75 cm²

Area of the image of the house formed on the screen = 1.55 m²

1 m = 100 cm = 10² cm

Area of the image of the house formed on the screen = 1.55 m² = 1.55 × (10² cm)²  = 1.55 × 10⁴ cm ²

Arial magnification

 = area of image / area of slide = 1.55 × 10⁴cm ²/1.75 cm²  = 0.8857 × 10⁴  

Linear magnifications

 = √(Arial magnification ) =√(0.8857 × 10⁴  ) = 0.9411 × 10² = 94.11