   Chapter 25, Problem 63PE

Chapter
Section
Textbook Problem

Referring to the electric room heater considered in the first example in this section, calculate the intensity of IR radiation in W/m2 projected by the concave mirror on a person 3.00 m away. Assume that the healing element radiates 1500 W and has an area of 100 cm2, and that half of the radiated power is reflected and focused by the mirror.

To determine

The intensity of IR radiation in W/m2 projected by the concave mirror on a person 3m away.

Explanation

Given info:

Image distance of the IR radiation, di=3.0m.

Radiating power of the heating element, P=1500W.

Area of the heating element, A=100cm2.

Half off the power is reflected and focused by the mirror.

Formula used:

Formula for radius of curvature of thin mirror is,

f=R2.... (1)

Here,

R is the radius of curvature.

Formula for focal length of thin mirror is,

1f=1d0+1di

Here,

• f is the focal length.
• d0 is the object distance.
• di is the image distance.

Rearranging the formula,

1d0=1f1di .... (2)

Formula for magnification is,

m=AA=dido

Here,

• mis the magnification.
• A is the area of the image.
• A is the area of the object.

Rearranging the formula,

A=mA .... (3)

Formula for intensity of the IR radiation is,

I=PA

Here,

• P is the power of the mirror.
• I is the intensity of the mirror.

Calculation:

Substitute 50cm for R in equation (1) to calculate the focal length.

f=502=25cm=0

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