Sherlock Holmes examines a clue by holding

his magnifying glass (with a focal length of
29.8 cm) 10.4 cm away from an object.

Find the image distance.
Answer in units of cm
Find the magnification.

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

1/f = 1/v - 1/u

where:
- f is the focal length of the lens,
- v is the image distance,
- u is the object distance

Given:
- The focal length (f) = 29.8 cm
- The object distance (u) = 10.4 cm

We can substitute these values into the lens formula:

1/29.8 = 1/v - 1/10.4

Next, we can simplify the equation:

1/v = 1/29.8 + 1/10.4
1/v = (10.4 + 29.8) / (10.4 * 29.8)
1/v = 40.2 / 308.32

Now, we can find the value of v by taking the reciprocal of both sides:

v = 308.32 / 40.2

Calculating this value, we find that v is approximately 7.66 cm.

So the image distance is approximately 7.66 cm.

Now, let's calculate the magnification.

The magnification (M) of an image formed by a lens is given by the formula:

M = -v/u

where:
- v is the image distance, and
- u is the object distance.

Given:
- The object distance (u) = 10.4 cm
- The image distance (v) = 7.66 cm

Now we can substitute these values into the formula:

M = -7.66 / 10.4

Calculating this value, we find that the magnification is approximately -0.738.

Therefore, the image distance is approximately 7.66 cm and the magnification is approximately -0.738.