Question

An object located 58.8 cm in front of a lens forms an image 63.1 cm behind the lens. Determine the focal length of the lens (in cm). Enter a number with two digits past the decimal point.

Answer 1

30.36 cm.

Step-by-step explanation:

To determine the focal length (f) of a lens, you can use the lens formula, which relates the object distance (d_o), image distance (d_i), and focal length:

1

�

=

1

�

�

+

1

�

�

f

1

​

=

d

o

​

1

​

+

d

i

​

1

​

Given:

Object distance (d_o) = 58.8 cm (positive because it's in front of the lens)

Image distance (d_i) = 63.1 cm (positive because it's behind the lens)

Now, plug in the values into the lens formula:

1

�

=

1

58.8

 

cm

+

1

63.1

 

cm

f

1

​

=

58.8cm

1

​

+

63.1cm

1

​

Calculate the right side of the equation:

1

�

=

0.0170

+

0.0159

f

1

​

=0.0170+0.0159

1

�

=

0.0329

f

1

​

=0.0329

Now, find the reciprocal to solve for

�

f:

�

=

1

0.0329

≈

30.36

 

cm

f=

0.0329

1

​

≈30.36cm

So, the focal length of the lens is approximately 30.36 cm.