A 18.3- cm focal-length lens is used to project 35- mm slidesonto a screen 4.17

Question

A 18.3- cm focal-length lens is used to project 35- mm slidesonto a screen 4.17 m from the projector lens. What must be thewidth of the screen ( m) if the image of the slide is to just fillthe screen? The width of the image on the slide is 34.3 mm. Any help would be greatly appreciated! A 18.3- cm focal-length lens is used to project 35- mm slidesonto a screen 4.17 m from the projector lens. What must be thewidth of the screen ( m) if the image of the slide is to just fillthe screen? The width of the image on the slide is 34.3 mm. Any help would be greatly appreciated!

Explanation / Answer

A 18.3- cm focal-length lens is used to project 35- mm slidesonto a screen 4.17 m from the projector lens. What must be thewidth of the screen ( m) if the image of the slide is to just fillthe screen? The width of the image on the slide is 34.3 mm. Any help would be greatly appreciated!
focal length=19.3cm
distance of the image=4.17m=v=417cm

size of the object=34.3mm=3.43cm
so size of the image=m*size of the object.
where m=magnification=image distance/object distance
to findout object distance u let us use the equation
1/u=1/f -1/v=1/19.3 -1/417=u=20.23cm
now m=417/20.23=20.61
hence the size of the image=width of the screen=20.61*34.3mm=707mm

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