Microscope Calculations | PDF - Free Printable

Let's solve each question step by step with clear explanations.

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1. Change the following measurements to microns (μm):

We know:
1 mm = 1000 μm

So, multiply each value by 1000.

a. 5.0 mm → 5.0 × 1000 = 5000 μm
b. 2.45 mm → 2.45 × 1000 = 2450 μm
c. 0.20 mm → 0.20 × 1000 = 200 μm
d. 0.03 mm → 0.03 × 1000 = 30 μm
e. 0.007 mm → 0.007 × 1000 = 7 μm
f. 1.04 mm → 1.04 × 1000 = 1040 μm

✔ Answers:
a. 5000 μm
b. 2450 μm
c. 200 μm
d. 30 μm
e. 7 μm
f. 1040 μm

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2. Change the following measurements to millimetres (mm):

We know:
1 μm = 0.001 mm, so divide by 1000.

a. 1765 μm → 1765 ÷ 1000 = 1.765 mm
b. 540.1 μm → 540.1 ÷ 1000 = 0.5401 mm
c. 1.1 μm → 1.1 ÷ 1000 = 0.0011 mm
d. 301.04 μm → 301.04 ÷ 1000 = 0.30104 mm
e. 7002 μm → 7002 ÷ 1000 = 7.002 mm
f. 49.7 μm → 49.7 ÷ 1000 = 0.0497 mm

✔ Answers:
a. 1.765 mm
b. 0.5401 mm
c. 0.0011 mm
d. 0.30104 mm
e. 7.002 mm
f. 0.0497 mm

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3. Give the total magnification for a microscope:

Total Magnification = Ocular × Objective

| OCULAR | OBJECTIVE | MAGNIFICATION |
|--------|-----------|---------------|
| x5 | x10 | 5 × 10 = 50x |
| x10 | x4 | 10 × 4 = 40x |
| x15 | x4 | 15 × 4 = 60x |
| x20 | x20 | 20 × 20 = 400x |

✔ Fill in the table:
- 50x
- 40x
- 60x
- 400x

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4. Calculate the H.P. field of view:

Given:
- L.P. magnification = ocular × objective = 5 × 10 = 50x
- L.P. field of view = 1.2 mm
- H.P. magnification = 5 × 40 = 200x

Field of view is inversely proportional to magnification.

So:

$$
\text{H.P. FOV} = \frac{\text{L.P. FOV} \times \text{L.P. mag}}{\text{H.P. mag}} = \frac{1.2 \times 50}{200} = \frac{60}{200} = 0.3 \text{ mm}
$$

Convert to μm: 0.3 mm = 300 μm

✔ Answer: 0.3 mm or 300 μm

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5. Microscope with ocular x15 and objectives x10 and x40

#### a. H.P. magnification?
H.P. = highest power → x15 × x40 = 600x

#### b. L.P. magnification?
L.P. = lowest power → x15 × x10 = 150x

#### c. If L.P. field of view is 3000 μm, calculate H.P. field of view

Use same formula:

$$
\text{H.P. FOV} = \frac{\text{L.P. FOV} \times \text{L.P. mag}}{\text{H.P. mag}} = \frac{3000 \times 150}{600} = \frac{450000}{600} = 750 \mu m
$$

✔ Answer: 750 μm

#### d. Size of a microbe if 12 fit across L.P. field of view

L.P. FOV = 3000 μm
Number of microbes = 12

Size of one microbe = $ \frac{3000}{12} = 250 \mu m $

✔ Answer: 250 μm

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6. What is the L.P. field of view of each microscope?

We are given diagrams with a millimetre rule visible in the field of view. We must estimate how many millimetres fit in the field based on the markings.

Let’s analyze each:

#### Microscope A:
- The rule has 4 divisions between two lines.
- Each division appears to be 1 mm (since it says "millimetre rule").
- The field shows 4 full divisions, so the diameter of the field is 4 mm.
- So, L.P. FOV = 4 mm = 4000 μm

#### Microscope B:
- Field shows 3 divisions of the rule.
- So, L.P. FOV = 3 mm = 3000 μm

#### Microscope C:
- Only 1 division visible.
- So, L.P. FOV = 1 mm = 1000 μm

✔ Answers:

| Microscope | mm | μm |
|-----------|-----|------|
| A | 4 mm | 4000 μm |
| B | 3 mm | 3000 μm |
| C | 1 mm | 1000 μm |

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7. If L.P. magnification in (A) is x100, calculate H.P. field of view using x5 ocular and x40 objective

First, clarify:
- L.P. magnification = x100 → this means ocular × objective = 100x
- But now we're using x5 ocular and x40 objective → total mag = 5 × 40 = 200x

So, this is H.P. magnification.

Now, from question 6, Microscope A has L.P. FOV = 4 mm (from diagram)

Now use:

$$
\text{H.P. FOV} = \frac{\text{L.P. FOV} \times \text{L.P. mag}}{\text{H.P. mag}} = \frac{4 \times 100}{200} = \frac{400}{200} = 2 \text{ mm}
$$

Wait — but FOV decreases as magnification increases, so 2 mm is larger than 4 mm? That can’t be.

✘ This suggests a problem: we are confusing what is L.P. and H.P.

But the question says: *"If the L.P. magnification in (A) above is x100"*, meaning that at low power (L.P.), magnification is 100x, and the FOV is 4 mm (from diagram).

Now, when switching to x5 ocular and x40 objective, total mag = 5 × 40 = 200x, which is higher than 100x, so this is H.P..

So:

$$
\text{H.P. FOV} = \frac{4 \times 100}{200} = 2 \text{ mm}
$$

But wait — 2 mm is larger than 4 mm, which doesn't make sense. So something is wrong.

Actually, let’s double-check: FOV is inversely proportional to magnification.

So higher magnification → smaller FOV.

So if L.P. FOV = 4 mm at 100x, then at 200x, FOV should be half → 2 mm.

Yes, that is correct.

Even though 2 mm < 4 mm, it’s still consistent.

But wait — is 2 mm possible?

Let’s think: at 100x, FOV = 4 mm
At 200x, FOV = 2 mm → yes, half.

So the calculation is correct.

✔ Answer: 2 mm

But let’s convert to μm: 2 mm = 2000 μm

But the question only asks for H.P. field of view — probably in mm.

✔ Final answer: 2 mm

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✔ Summary of All Answers:

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1. Convert to microns (μm):
a. 5000 μm
b. 2450 μm
c. 200 μm
d. 30 μm
e. 7 μm
f. 1040 μm

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2. Convert to millimetres (mm):
a. 1.765 mm
b. 0.5401 mm
c. 0.0011 mm
d. 0.30104 mm
e. 7.002 mm
f. 0.0497 mm

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3. Total Magnification:
- 50x
- 40x
- 60x
- 400x

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4. H.P. field of view:
→ 0.3 mm or 300 μm

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5.
a. H.P. magnification: 600x
b. L.P. magnification: 150x
c. H.P. FOV: 750 μm
d. Microbe size: 250 μm

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6. Field of View (based on diagrams):
| Microscope | mm | μm |
|-----------|-----|------|
| A | 4 mm | 4000 μm |
| B | 3 mm | 3000 μm |
| C | 1 mm | 1000 μm |

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7. H.P. field of view for (A) using x5 and x40:
→ 2 mm

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