Question

Sitting beside a spherical glass ornament, you notice that your face is reflected inthe sphere. The image appears 5.2 cm behind the ornament when you are 17 cmin front of it. What is the ornament’s focal length and radius of curvature?

Answer 1

To determine the focal length we will use the following formula:

`(1)/(d_0)+(1)/(d_i)=(1)/(f)`

Where:

`\begin{gathered} d_0=\text{ distance of the object} \\ d_i=\text{ distance of the image} \\ f=\text{ focal length} \end{gathered}`

Now, we solve for "f". To do that we will add the fractions on the left side:

`(d_i+d_0)/(d_0d_i)=(1)/(f)`

Now, we invert both sides:

`(d_0d_i)/(d_i+d_0)=f`

Substituting the values:

`((17cm)(5.2cm))/(17m+5.2cm)=f`

Solving the operations:

`3.98cm=f`

Therefore, the focal length is 3.98 cm.

The focal length and the radius are related by the following formula:

`r=2f`

Where "r" is the radius. Substituting the value we get:

`r=2(3.98cm)`

Solving the operations:

`r=7.96cm`

Therefore, the radius of curvature is 7.96 cm.