Question

Find the focal length of contact lenses that would allow a nearsighted person with a 130 cm far point to focus on the stars at night. Express your answer to three significant figures.

A) 43.3 cm
B) 86.7 cm
C) 130 cm
D) 260 cm

Answer 1

The focal length of the contact lense is 130 cm. Option C.

The focal length (f) of a lens can be calculated using the lens formula:

`\[ (1)/(f) = (1)/(d_o) - (1)/(d_i) \]`

where:

f is the focal length,

d_o is the object distance,

d is the image distance.

In this case, the object distance
`(\( d_o \))` is the near point distance, which is 130 cm (far point). To focus on the stars at night, the image distance
`(\( d_i \))` is essentially at infinity.

`\[ (1)/(f) = \frac{1}{130 \, \text{cm}} - (1)/(\infty) \]`

Since the second term on the right side tends to zero, the equation simplifies to:

`\[ (1)/(f) = \frac{1}{130 \, \text{cm}} \]`

Now, solving for \( f \):

`\[ f = \frac{130 \, \text{cm}}{1} = 130 \, \text{cm} \]`

So, the correct answer is:

C) 130 cm