Question

you place a object 23cm in front of a diverging lens which has a focal length with magnitude of 13.4cm. determine how far the object should be placed to reduce image size by factor of 4.35

Answer 1

Answer on Question #69312, Physics / Optics

you place a object 23cm in front of a diverging lens which has a focal length with magnitude of 13.4cm. determine how far the object should be placed to reduce image size by factor of 4 35

Find: $d_0$ - ?

Given:

$f = 13.4$ cm

$K = 4.35$

Solution:

If the distances from the object to the lens and from the lens to the image are $d_0$ and $d_i$ respectively, for a lens of negligible thickness, in air, the distances are related by the thin lens formula:

$$\frac{1}{d_0} - \frac{1}{d_i} = -\frac{1}{f}(1),$$

where $f$ is focal length of a diverging lens

Magnification of lens:

$$M = \frac{d_i}{d_0}(2)$$

According to the condition of the task: $M = \frac{1}{4.35} = 0.23(3)$

Of $(2) \Rightarrow d_i = M d_0(4)$

(4) in (1): $\frac{1}{d_0} - \frac{1}{M d_0} = -\frac{1}{f}(5)$

Of $(5) \Rightarrow \frac{M - 1}{M d_0} = -\frac{1}{f}(6)$

Of $(6) \Rightarrow d_0 = -\frac{(M - 1) f}{M}(7)$

Of $(7) \Rightarrow d_0 = 44.86$ cm

Answer:

44.86 cm

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