Problem 3 on Units & Dimensions

Description:

Problem

The photograph of a house occupies an area of 1.75 cm² on a 35mm 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

Visualizing the problem first,

Now, Areal magnification is the enlargement of area the image undergoes.

Area Magnification = Area of Image on the screen/Area of Image on the slide

Linear magnification, is the enlargement of linear dimensions the image undergoes.

Linear Magnification = √Areal Magnification

Let’s understand the formula for Linear Magnification by an illustration −

• The first square has an area of, l², and edge length, l.
• Second square has an area of, 2l², and edge length, √l

Therefore,

Areal Magnification = 2l²/l² = 2

Linear Magnification = √2l/l = √2

Clearly, we can see,

Linear Magnification = √Areal Magnification

Solving the problem,

Areal Magnification = Area of Image on the screen/Area of Image on the slide

Hence,

Areal Magnification = 1.55 m²/1.75 cm² = 1.55 × 10⁴/1.75

Now,

Linear Magnification = √Areal Magnification

Linear Magnification = √1.55 × 10⁴/1.75 = 0.941 × 10²

Hence,

Linear Magnification = 94.1

Important Note − The result of linear magnification contains 3 significant digits. This is because the original multiplicands contain only 3 significant digits.