BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.5, Problem 114E
To determine

The distance of the object from the lens.

Expert Solution

Answer to Problem 114E

The distance of the object from the lens is 12cm_.

Explanation of Solution

Given:

The equation that relates F, x and y is 1F=1x+1y, where F is the focal length of the convex lens, x is the distance of the object from the lens and y is the  distance of the image from the lens.

Formula used:

Quadratic formula:

The solution of a quadratic equation of the form ax2+bx+c=0,a0 can be obtained by using the quadratic formula x=b±b24ac2a.

Calculation:

The focal length of convex lens is 4.8cm.

Since the image of an object is 4 cm closer to the lens than the object itself, it can be written that y=x4.

Substitute 4.8 for F and x4 for y in the equation 1F=1x+1y.

14.8=1x+1x414.8=x4+xx(x4)14.8=2x4x(x4)x(x4)=4.8(2x4)

Simplify the above equation as follows.

x24x=9.6x19.2x24x9.6x+19.2=0x213.6x+19.2=0

Compare this equation with the general form ax2+bx+c=0.

Here a=1,b=13.6and c=19.

Use the quadratic formula to obtain the roots of the given equation.

x=(13.6)±(13.6)24×1×192×1=13.6±184.96762=13.6±108.962=13.6±10.42

Simplify further as follows.

x=13.6+10.42or x=13.610.42x=242or x=3.22x=12or x=1.6

Substitute x=12 in y=x4.

y=124=8

Substitute x=1.6 in y=x4.

y=1.64=2.4

Note that, the distance cannot be negative.

Thus, the distance of the object from the lens is 12cm_.

Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!