Projection Lantern

A projection lantern uses a lens to project an enlarged image of a small object (e.g. a slide) onto a screen. The magnification (M) is a measure of how much larger (or smaller) the image appears compared to the original object.

Formula for magnification:

Magnification is given by:

$M = \frac{v}{u}$

Where:

• $M$ = magnification
• $v$ = image distance (distance from lens to screen)
• $u$ = object distance (distance from lens to slide)

Also,

$M = \frac{h_i}{h_o}$

Where:

• $h_i$ = height (or size) of image
• $h_o$ = height (or size) of object (slide)

Example

A projection lantern uses a slide of size 2 cm × 2 cm to project an image of size 100 cm × 100 cm onto a screen 12 m (1200 cm) away from the lens.

Find:

1. How far from the lens the slide must be (object distance $u$)
2. The approximate focal length of the projection lens.

Step 1: Calculate magnification

$M = \frac{h_i}{h_o} = \frac{100}{2} = 50$

Also from magnification formula:

$M = \frac{v}{u}$

So:

$\frac{v}{u} = 50 \quad \Rightarrow \quad u = \frac{v}{50} = \frac{1200}{50} = 24 \, \text{cm}$

Answer:

Object distance $u = 24 \, \text{cm}$

Step 2: Find focal length (f)

Use the lens formula:

$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$

$\frac{1}{f} = \frac{1}{1200} + \frac{1}{24}$

Convert to common denominator:

$\frac{1}{f} = \frac{1 + 50}{1200} = \frac{51}{1200}$

$f = \frac{1200}{51} \approx 23.53 \, \text{cm}$

• Focal length of lens = approximately 23.5 cm

1. Projection of films, slides and transparencies,
2. projection of opaque objects, i.e. episcopacy projection,
3. used in searchlights and headlights,
4. used in projection apparatus in industry for gauge and screw thread testing,
5. used in physical experiments such as projection of a spectrum,
6. used in polarization experiments and interference experiments