Igcse Model Questions Vol1 2019 Physics Question 35

A converging lens of focal length 20 cm is used to form an image of a distant street lamp on a screen. A thin glass plate of thickness 2.0 mm and refractive index 1.50 is placed directly in front of the screen, covering the image. The plate causes the image to shift. (i) Determine the new position of the screen relative to the lens to bring the image back into focus. (ii) The lens material shows chromatic dispersion described by \(f(\lambda)=f_0\bigl[1+k\frac{\lambda-\lambda_0}{\lambda_0}\bigr]\) where \(f_0=20\) cm at \(\lambda_0=550\) nm and \(k=0.02\). Calculate the separation on the screen between the images formed by red light (\(\lambda=700\) nm) and blue light (\(\lambda=450\) nm). Give the separation in millimetres.