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} (1)/(d_i)+(1)/(d_o)=(1)/(f) \\ m=-(d_i)/(d_o)=(s_i)/(s_o) \end{gathered}`

Solution:

`\begin{gathered} (1)/(d_i)+(1)/(30)=(1)/(-20) \\ (1)/(d_i)=-(1)/(20)-(1)/(30) \\ (1)/(d_i)=-(3)/(60)-(2)/(60)_{} \\ (1)/(d_i)=(-5)/(60) \\ (1)/(d_i)=(1)/(-12) \\ d_i=-12\text{ cm} \\ \\ m=-(d_i)/(d_o)=-(-12)/(30)=(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)