Question

An object is 14 cm from a biconvex lens. The focal distance of the lens is 30 cm. What is the image
distance from the lens, di? (1 point)

26.25

-12.25

-26.25

12.25

Answer 1

To find the image distance (\(d_i\)) from a biconvex lens, we can use the lens formula:

\[
\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}
\]

Where:
- \(f\) is the focal length of the lens (positive for a biconvex lens),
- \(d_o\) is the object distance (positive if the object is on the same side as the incoming light),
- \(d_i\) is the image distance (positive if the image is on the opposite side of the lens from the object).

Given:
- \(d_o = 14 \, \text{cm}\)
- \(f = 30 \, \text{cm}\)

Now, apply the values to the lens formula:

\[
\frac{1}{30} = \frac{1}{14} + \frac{1}{d_i}
\]

First, let's calculate \(\frac{1}{14}\):

\[
\frac{1}{14} \approx 0.0714
\]

Now substituting in the equation:

\[
\frac{1}{30} \approx 0.0333
\]

Now rearranging the lens formula:

\[
\frac{1}{d_i} = \frac{1}{30} - \frac{1}{14}
\]

Calculating the right side:

\[
\frac{1}{d_i} = 0.0333 - 0.0714
\]

Now solving for \(\frac{1}{d_i}\):

Converting both fractions to have a common denominator (for instance, 210):

\[
\frac{1}{30} = \frac{7}{210}, \quad \frac{1}{14} = \frac{15}{210}
\]

Now substituting:

\[
\frac{1}{d_i} = \frac{7}{210} - \frac{15}{210} = \frac{7 - 15}{210} = \frac{-8}{210}
\]

Now we simplify:

\[
\frac{-8}{210} = \frac{-4}{105}
\]

Taking the reciprocal to find \(d_i\):

\[
d_i = -\frac{105}{4} = -26.25 \, \text{cm}
\]

Thus, the image distance \(d_i\) is:

\(-26.25\)

So your answer is:

\(-26.25\) (the negative sign indicates that the image is on the same side as the object).