Sherlock Holmes examines a clue by holding

his magnifying glass (with a focal length of
26.5 cm) 15.1 cm away from an object.
Find the image distance.
Answer in units of cm

11.4 cm

To find the image distance, we can use the lens formula:

1/f = 1/do + 1/di

where:
- f is the focal length of the lens (26.5 cm in this case),
- do is the object distance (15.1 cm in this case),
- di is the image distance (unknown).

Plugging in the given values, we get:

1/26.5 = 1/15.1 + 1/di

Now, we can solve for di by rearranging the equation:

1/di = 1/26.5 - 1/15.1

To simplify the equation, we can find a common denominator:

1/di = (15.1 - 26.5)/(26.5 * 15.1)

Calculating the numerator and denominator:

1/di = (-11.4)/(398.15)
1/di = -0.0287

To isolate di, we can take the reciprocal of both sides:

di = 1/(-0.0287)

Calculating di:

di ≈ -34.8 cm

The image distance is approximately -34.8 cm.

To find the image distance, we can use the lens formula:

1/f = 1/dₒ + 1/dᵢ

where:
- f is the focal length of the lens
- dₒ is the object distance (distance of the object from the lens)
- dᵢ is the image distance (distance of the image from the lens)

Given:
- f = 26.5 cm (focal length)
- dₒ = 15.1 cm (object distance)

Substituting these values into the lens formula, we get:

1/26.5 = 1/15.1 + 1/dᵢ

To solve for dᵢ, we need to rearrange the equation. First, let's find the common denominator of 15.1 and 26.5, which is 397.15.

Now, the equation becomes:

(397.15 + 26.5) / (26.5 * 15.1) = 1/dᵢ

423.65 / 400.15 = 1/dᵢ

To solve for dᵢ, we take the reciprocal of both sides:

dᵢ = 400.15 / 423.65

Evaluating this expression, we find that the image distance is approximately 0.945 cm.