Magnification and specimen size

1. Which expression correctly defines magnification when image size and actual size are corresponding lengths in the same unit?

Answer A: image size ÷ actual size

Magnification equals image size divided by actual size. Using the same unit makes the length units cancel, so the answer is a unit-free scale factor written with × notation.

2. Convert an actual specimen length of 0.38 mm to micrometres. No magnification calculation is required.

Answer C: 380 μm

Multiply a millimetre value by 1000: 0.38 × 1000 = 380. The actual specimen length is 380 μm; conversion changes the unit, not the physical length.

3. Convert an actual specimen length of 460 μm to millimetres. No image resizing is involved.

Answer B: 0.46 mm

Since 1 mm = 1000 μm, divide 460 by 1000. This gives 0.46 mm. Multiplying instead would make the numerical value larger when changing to the larger unit.

4. An unresized image has a corresponding specimen length of 60 mm at ×150. What is the actual length in millimetres?

Answer D: 0.4 mm

Actual size = 60 mm ÷ 150 = 0.4 mm. The check 0.4 mm × 150 = 60 mm reproduces the stated image length and confirms the rearrangement.

5. A specimen is actually 0.08 mm long and its corresponding length is 32 mm in an unresized image. What is the magnification?

Answer A: ×400

Magnification = 32 mm ÷ 0.08 mm = 400, so the answer is ×400. Magnification has no length unit because the matching millimetre units cancel.

6. A specimen is actually 25 μm long and has a stated image length of 15 mm. The image is unresized. What is its magnification?

Answer C: ×600

The actual length is 25 μm = 0.025 mm. Magnification = 15 mm ÷ 0.025 mm = 600, so the image magnification is ×600.

7. A specimen is actually 0.12 mm wide and is represented at ×250. The image is not resized. What is the corresponding image width?

Answer B: 30 mm

Image size = 250 × 0.12 mm = 30 mm. Dividing would calculate in the wrong direction because an image at ×250 must be larger than the actual specimen.

8. An unresized image length is 84 mm and the corresponding actual specimen length is 70 μm. What is the magnification?

Answer D: ×1200

Seventy micrometres is 0.070 mm. Magnification = 84 mm ÷ 0.070 mm = 1200, so the correct scale factor is ×1200.

9. A scale bar measures 12 mm on an unresized image and represents an actual distance of 30 μm. What is the image magnification? All needed measurements are stated here.

Answer A: ×400

The scale bar compares 12 mm on the image with 30 μm = 0.030 mm actually. Magnification = 12 ÷ 0.030 = 400, giving ×400.

10. A corresponding length is stated as 45 mm in an unresized image at ×900. What is the actual specimen length in micrometres?

Answer C: 50 μm

Actual size = 45 mm ÷ 900 = 0.05 mm. Multiplying by 1000 converts this to 50 μm. The reverse check is 0.05 mm × 900 = 45 mm.

11. An unresized image length is 2.4 mm and the corresponding actual length is 40 μm. What is the magnification?

Answer B: ×60

Forty micrometres equals 0.040 mm. Magnification = 2.4 mm ÷ 0.040 mm = 60, so the image is at ×60. Matching the units before division makes this a valid scale comparison.

12. A specimen is actually 6 μm long and is represented at ×2500 without later resizing. What is the image length in millimetres?

Answer D: 15 mm

Image size = 2500 × 0.006 mm = 15 mm. A check in micrometres gives 2500 × 6 = 15000 μm, which is also 15 mm.

13. Specimen A has image length 36 mm at ×600. Specimen B has image length 20 mm at ×250. Both images are unresized and each length covers the whole corresponding specimen. Which specimen is actually longer?

Answer A: Specimen B

A is 36 ÷ 600 = 0.06 mm. B is 20 ÷ 250 = 0.08 mm. Therefore specimen B is actually longer, even though its stated image length is shorter.

14. Convert an actual width of 0.0075 mm to micrometres before using it in a calculation.

Answer C: 7.5 μm

The conversion is 0.0075 mm × 1000 = 7.5 μm. The decimal shifts three places because one millimetre contains one thousand micrometres.

15. Convert an actual length of 1250 μm to millimetres before comparing it with an image measurement.

Answer B: 1.25 mm

The conversion is 1250 μm ÷ 1000 = 1.25 mm. This is the same physical length expressed using the larger millimetre unit.

16. An unresized image length is 9 mm and the corresponding actual length is 3 μm. What is the magnification?

Answer D: ×3000

Three micrometres is 0.003 mm. Magnification = 9 mm ÷ 0.003 mm = 3000, so the result is ×3000. The millimetre units cancel after conversion.

17. An unresized image shows a corresponding length of 48 mm for a specimen that is actually 0.16 mm long. What is the magnification?

Answer A: ×300

Magnification = 48 mm ÷ 0.16 mm = 300. The correct answer is ×300, and 0.16 mm × 300 checks back to 48 mm.

18. An original image at ×800 has a stated length of 20 mm. It is enlarged uniformly so all linear image lengths become 1.5 times as long; the specimen is unchanged. What is the new magnification?

Answer C: ×1200

The new magnification is 800 × 1.5 = ×1200. The image length becomes 30 mm while the actual specimen length remains 20 ÷ 800 = 0.025 mm; 30 ÷ 0.025 also equals 1200.

19. A corresponding image length is 72 mm at ×240, with no later resizing. What is the actual length in micrometres?

Answer B: 300 μm

Actual size = 72 mm ÷ 240 = 0.3 mm. Converting gives 0.3 × 1000 = 300 μm, so the correct actual length is 300 μm.

20. A scale bar measures 5 mm on an unresized image and represents 2 μm actually. What is the magnification? The bar measurements are fully stated.

Answer D: ×2500

The actual represented length is 2 μm = 0.002 mm. Magnification = 5 mm ÷ 0.002 mm = 2500, so the image is at ×2500.

21. A specimen is actually 14 μm long and is represented at ×500 without resizing. What is the corresponding image length in millimetres?

Answer A: 7 mm

Image size = 500 × 0.014 mm = 7 mm. Equivalently, 500 × 14 μm = 7000 μm, which converts to 7 mm. Both unit routes produce the same image length.

22. An unresized image length is 27 mm at ×90. What is the corresponding actual length in micrometres?

Answer C: 300 μm

Actual size = 27 mm ÷ 90 = 0.3 mm. Multiplying by 1000 gives 300 μm. Substitution confirms that 0.3 mm × 90 = 27 mm.

23. Which rearrangement finds actual size from a stated image size and magnification, provided the image and actual lengths use compatible units?

Answer B: actual size = image size ÷ magnification

Actual size equals image size divided by magnification. This makes the actual length smaller than the image length when magnification is greater than ×1, as expected.

24. Why must image size and actual size be converted to the same length unit before magnification is calculated?

Answer D: So the equal length units cancel and the numerical ratio is valid

Corresponding lengths must use the same unit so their units cancel and the ratio correctly compares like with like. Magnification is then a unit-free scale factor, commonly written with × notation.