Question

A +2.5 cm focal length lens is used to project the image of a slide onto a screen. The lens is 3.0 m from the screen and the screen is 1.5 m wide and 0.5 m high.

Part A)

How far should the slide be from the lens to produce a crisp image on the screen?

Part B)

What are the dimensions of the slide (i.e. width and height) that would make an image that fills the entire screen?

Answer 1

• To get a sharper image the object must be placed at focal distance f.
• Since it is a convex lens the image obtained is inverted.
• Len's makers formula
• $\frac{1}{V} - \frac{1}{U} = \frac{1}{f}$
• 
  Focal length f = +2.5cm 0.025m VE + 3.0m By lens makers formula =- ū u f There fore ; Yu = '/v- Ys Yuf-v j fv fv 0.025 3 f-v 0.025 - 3 1.02521m =(-0·0257m a so the slide should be placed at distance 0.025m to the left of the lens to get crisp image on screen
  
• 
  * The dimensions of slide which can fill up the screen can be found out by the equation. M = V u ale-120 W - (0.025) (The -ve sign indicates image is enverted). so the slide is magnified 120 times and the image is obtained onventdly. - To fill up screen; GASKO Cros 12 0x (object size) - screen size. => 720 X (object size ) = 1.5 * 0.5 object size = 1.5x0.5 6.25x 103 m2 12oot Area of slide 6.25 *10-3 m 2 ) 3 3) Screen ; height width 1.5 0.5 = 2 x width de height HXW= 3WX we Area of slide 6.25*10-3 m2
  
• 
  zo 2012 (36) 3W2 = 6.25*10-3 W2=2.0833x10-3 ot ad noo doon W = 0.0 4 5 6 43 m Dos Height 6.25 *10-3 width Sony Ogizar- = 6.25 x 10-3 20013693m 30.045643 Height = 0.13693m width = 0.045 643 m aan do 1) XS 0 = 1 bila te on