91Ó°ÊÓ

The focal length is the distance between a convex lens or a concave mirror and the focal point of a lens or mirror. It is the point at which two parallel light beams meet or converge. Depending on the lens and mirror (concave or convex), the focal length varies with the sign (positive or negative).

(a)

Use the thin lens equation for the focal length:

$\frac{1}{f}=\frac{1}{d_i}+\frac{1}{d_{∘}}$.

Rearranging the expression and substituting the values –

$$\begin{gathered} \frac{1}{d_{∘}}=\frac{1}{f}-\frac{1}{d_i} \\ {d}_{∘}={\left(\frac{1}{22.0×{10}^{-3}m}-\frac{1}{33.0×{10}^{-3}m}\right)}^{-1} \\ =0.066m \\ =0.066×1000mm \\ =66.0mm \end{gathered}$$

Therefore, the value for distance is obtained as $d_{∘}=66.0mm$.

(b)

Use the equation of the magnification that relates the image distance to the object distance: .

Substituting the values and evaluating –

$$\begin{gathered} m=-\frac{d_i}{d_{∘}} \\ =-\frac{0.033m}{0.066m} \\ =-\frac{1}{2} \end{gathered}$$

Therefore, the value for magnification is obtained as $m=-\frac{1}{2}$.