Question

A 10-cm high object is placed 30 cm in front of a concave lens with a focal length of -20 cm. Determine the image distance magnification. Enumerate the characteristics of the image produced. Must follow the GRESA format.Given:Required:Equation(s) Needed:Solution: Final answers:L-ocation:O-rientation:S-ize:T-ype

Answer 1

Given:

object distance (do) = 30 cm

object size (so) = 10 cm

focal length (f) = - 20 cm

Required:

image distance (di),

magnification (m)

image characteristics.

Equations:

$\begin{gathered} \frac{1}{d_i}+\frac{1}{d_o}=\frac{1}{f} \\ m=-\frac{d_i}{d_o}=\frac{s_i}{s_o} \end{gathered}$

Solution:

$\begin{gathered} \frac{1}{d_i}+\frac{1}{30}=\frac{1}{-20} \\ \frac{1}{d_i}=-\frac{1}{20}-\frac{1}{30} \\ \frac{1}{d_i}=-\frac{3}{60}-\frac{2}{60}_{} \\ \frac{1}{d_i}=\frac{-5}{60} \\ \frac{1}{d_i}=\frac{1}{-12} \\ d_i=-12\text{ cm} \\ \\ m=-\frac{d_i}{d_o}=-\frac{-12}{30}=\frac{2}{5} \end{gathered}$

Location: 12 cm "inside" the mirror (di = -12 cm)

Orientation: Upright (m > 0)

Size: si = 4 cm (object size multiplied by m)

Type: Virtual image (di < 0)