A converging lens is used to project a 250 mm image of a square slide onto a screen 1000 mm away. the focal length of the lens is 200 mm. by means of scale drawing, determine---(a) the distance of the slide from the lens----(b) the size of the slide???

Question

please explain it to me...

Julia Aguilar · Accepted Answer

(a)Distance of the slide from lens = 250 mm

(b) The size of the slide = 62.5 mm

Given

#s_i->"Size of the image"=250mm#
#v->"Image distance"=+1000mm#
#f-> "Focal length of convex lens"=+200mm#

We are to find out

#u->"object distance"=?#

#s_o->"Size of the object"=?#
Calculation
Lens formula
#color(blue)(1/v-1/u=1/f)#
Plugging the values

#=>1/1000-1/u=1/200#
#=>1/u=1/1000-1/200=(1-5)/1000=-1/250#
#color(red)(=>u=-250mm)#
#color(green)("-ve sign means real object")#
Now magnification (m)

#m = s_i/s_o=v/u#
#=>250/s_o=1000/250=4#
#color(red)(=>s_o=250/4=62.5mm)#
The distance of the slide from lens (u)=250mm.

The size of the slide =62.5mm

Xavier Adame · Answer

undefined (a) The distance of the slide from the lens is 350 mm.

(b) The size of the slide is 175 mm.

HIX Tutor · Answer

undefined To solve this, let's go step by step.

### (a) Distance of the slide from the lens

1. **Identify the given information:**
   - Image size $ h_i = 250 $ mm
   - Screen distance from the lens $ v = 1000 $ mm
   - Focal length $ f = 200 $ mm

2. **Use the lens formula:**
   $$
   \frac{1}{f} = \frac{1}{v} + \frac{1}{u}
   $$
   where $ u $ is the distance of the slide from the lens.

3. **Rearrange the formula to find $ u $:**
   $$
   \frac{1}{u} = \frac{1}{f} - \frac{1}{v}
   $$

4. **Plug in the values:**
   $$
   \frac{1}{u} = \frac{1}{200} - \frac{1}{1000}
   $$

5. **Calculate $ \frac{1}{200} $ and $ \frac{1}{1000} $:**
   - $ \frac{1}{200} = 0.005 $
   - $ \frac{1}{1000} = 0.001 $

6. **Subtract:**
   $$
   \frac{1}{u} = 0.005 - 0.001 = 0.004
   $$

7. **Find $ u $:**
   $$
   u = \frac{1}{0.004} = 250 \text{ mm}
   $$

### (b) Size of the slide

1. **Use the magnification formula:**
   $$
   \text{Magnification} (M) = \frac{h_i}{h_o} = -\frac{v}{u}
   $$
   Where $ h_o $ is the size of the slide.

2. **Rearrange for $ h_o $:**
   $$
   h_o = \frac{h_i \times u}{v}
   $$

3. **Plug in the values:**
   $$
   h_o = \frac{250 \times 250}{1000}
   $$

4. **Calculate:**
   $$
   h_o = \frac{62500}{1000} = 62.5 \text{ mm}
   $$

### Final Answers
- (a) Distance of the slide from the lens = **250 mm**
- (b) Size of the slide = **62.5 mm**