A student did an experiment with a convex lens. He put an object at different distances 25 cm, 30 cm, 40 cm, 60 cm and 120 cm from the lens. In each case he measured the distance of the image from the lens. His results were 100 cm, 24 cm, 60 cm, 30 cm and 40 cm, respectively.
Unfortunately, his results are written in wrong order.
(a) Rewrite the image distances in the correct order.
(b) What would be the image distance if the object distance was 90 cm?
(c) Which of the object distances gives the biggest image?
(d) What is the focal length of this lens?
(a) 100 cm; 60 cm, 40 cm, 30 cm, 24 cm
(b) u = -25 cm
v = 100 cm
\(\frac{1}{v}\) - \(\frac{1}{u}\) = \(\frac{1}{f}\)
\(\frac{1}{100}\) - \(\frac{1}{-25}\) = \(\frac{1}{0.20}\)
\(\frac{1}{f}\) = \(\frac{5}{100}\)
f = 20 cm
u = -90 cm
v = ?
\(\frac{1}{v}\) - \(\frac{1}{u}\) = \(\frac{1}{f}\)
\(\frac{1}{v}\) - \(\frac{1}{-90}\) = \(\frac{1}{20}\)
\(\frac{1}{v}\) = \(\frac{1}{20}\) - \(\frac{1}{90}\)
\(\frac{1}{v}\) = \(\frac{7}{180}\)
v = 25.7 cm
(c) 25 cm
(d) 20 cm (AS calculated in below)
u = -25 cm
v = 100 cm
\(\frac{1}{v}\) - \(\frac{1}{u}\) = \(\frac{1}{f}\)
\(\frac{1}{100}\) - \(\frac{1}{-25}\) = \(\frac{1}{0.20}\)
\(\frac{1}{f}\) = \(\frac{5}{100}\)
f = 20 cm