Question

Review Part A An object is 29.0 cm from a screen What are the radi of a symmetric converging plastic lens (ie, two equally ourved surtaces) that will form an image on the screen twice the height of the object? (Take the index of refraction of plastic to be 1.59.) Express your answer with the appropriate units.

Answer 1

Answer:

R = 22.81 cm

Explanation:

As we know that distance of object from screen is 29 cm

$d_i + d_o = 29 cm$

also we know that

$M = -2$ (since its a real image so magnification must be negative)

$\frac{d_i}{d_o} = -2$

$d_i = -2d_o$

now we have

$-2d_o + d_o = 29$

$d_o = -29 cm$

now by lens formula

$\frac{1}{d_i} + \frac{1}{d_o} = \frac{1}{f}$

$\frac{1}{58} + \frac{1}{29} = \frac{1}{f}$

$f = 19.33 cm$

now we know by lens maker's formula

$\frac{1}{f} = (\mu - 1)(\frac{2}{R})$

$\frac{1}{19.33} = (1.59 - 1)(\frac{2}{R})$

R = 22.81 cm