Chapter 25, Problem 63PE

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000

Chapter
Section

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000
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=3.0â€„m.

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

Area of the heating element, A=100â€„cm2.

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

Formula used:

Formula for radius of curvature of thin mirror is,

â€ƒâ€ƒf=R2.... (1)

Here,

R is the radius of curvature.

Formula for focal length of thin mirror is,

â€ƒâ€ƒ1f=1d0+1di

Here,

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

Rearranging the formula,

â€ƒâ€ƒ1d0=1fâˆ’1di .... (2)

Formula for magnification is,

â€ƒâ€ƒm=Aâ€²A=âˆ’dido

Here,

• mis the magnification.
• Aâ€² is the area of the image.
• A is the area of the object.

Rearranging the formula,

â€ƒâ€ƒAâ€²=mA .... (3)

Formula for intensity of the IR radiation is,

â€ƒâ€ƒI=PAâ€²

Here,

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

Calculation:

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

â€ƒâ€ƒf=502=25â€„cm=0

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