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Microscope and Microscopy - Types of Microscopes-advanced

Grade 9CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Magnification: This is the process of enlarging the apparent size of an object. It is calculated as the ratio of the image height to the object height, represented by M=IOM = \frac{I}{O}.

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Resolving Power (Resolution): The ability of an optical instrument to show two close points as separate entities. The limit of resolution dd is determined by the wavelength of light λ\lambda and the numerical aperture NANA. Smaller dd means higher resolution.

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Compound Light Microscope: Uses visible light (wavelength λ≈400 nm\lambda \approx 400\text{ nm} to 700 nm700\text{ nm}) and glass lenses. The maximum useful magnification is usually limited to 1500×1500\times to 2000×2000\times due to the diffraction limit of light.

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Transmission Electron Microscope (TEM): Uses a beam of electrons instead of light. Because the wavelength of electrons is significantly shorter than visible light (approx 0.005 nm0.005\text{ nm}), TEM can achieve magnifications up to 1,000,000×1,000,000\times and resolutions of 0.1 nm0.1\text{ nm} to 0.2 nm0.2\text{ nm}. It provides 22D images of internal cell structures.

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Scanning Electron Microscope (SEM): Scans the surface of a specimen coated with a thin layer of metal (like gold). It provides highly detailed 33D images of the surface topography.

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Numerical Aperture (NANA): A dimensionless number that characterizes the range of angles over which the system can accept or emit light. It is given by NA=nsin⁡θNA = n \sin \theta, where nn is the refractive index of the medium.

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Comparison: Light microscopes can view living cells in color, whereas electron microscopes require a vacuum, meaning only dead/fixed specimens can be viewed in black and white (often false-colored later).

📐Formulae

Mtotal=Mobjective×MeyepieceM_{\text{total}} = M_{\text{objective}} \times M_{\text{eyepiece}}

M=Size of ImageActual Size of ObjectM = \frac{\text{Size of Image}}{\text{Actual Size of Object}}

d=0.61λNAd = \frac{0.61 \lambda}{NA}

1 mm=103 μm=106 nm1\text{ mm} = 10^3\ \mu\text{m} = 10^6\ \text{nm}

💡Examples

Problem 1:

A student is observing a plant cell using a compound microscope. The ocular lens has a magnification of 10×10\times and the high-power objective lens has a magnification of 45×45\times. Calculate the total magnification of the specimen.

Solution:

Mtotal=Meyepiece×MobjectiveM_{\text{total}} = M_{\text{eyepiece}} \times M_{\text{objective}} Mtotal=10×45M_{\text{total}} = 10 \times 45 Mtotal=450×M_{\text{total}} = 450\times

Explanation:

To find the total magnification in a compound microscope, the magnifying powers of the individual lenses (eyepiece and objective) are multiplied together.

Problem 2:

An electron micrograph shows a bacterium that measures 5 cm5\text{ cm} in the photograph. If the actual size of the bacterium is 2 μm2\ \mu\text{m}, what is the magnification used?

Solution:

First, convert all units to micrometers (μm\mu\text{m}): Size of Image=5 cm=50 mm=50,000 μm\text{Size of Image} = 5\text{ cm} = 50\text{ mm} = 50,000\ \mu\text{m} Actual Size=2 μm\text{Actual Size} = 2\ \mu\text{m} Now, apply the magnification formula: M=Image SizeActual SizeM = \frac{\text{Image Size}}{\text{Actual Size}} M=500002M = \frac{50000}{2} M=25000×M = 25000\times

Explanation:

Magnification is the ratio of the measured image size to the actual size. Consistent units (micrometers in this case) must be used for the calculation.

Problem 3:

A microscope has a limit of resolution of 0.2 μm0.2\ \mu\text{m}. Can this microscope be used to clearly distinguish two points that are 150 nm150\ \text{nm} apart?

Solution:

Convert the limit of resolution to nanometers: 0.2 μm=0.2×1000 nm=200 nm0.2\ \mu\text{m} = 0.2 \times 1000\ \text{nm} = 200\ \text{nm} Distance between points = 150 nm150\ \text{nm}. Since 150 nm<200 nm150\ \text{nm} < 200\ \text{nm}, the points are closer than the limit of resolution.

Explanation:

If the distance between two objects is less than the limit of resolution (dd) of the microscope, they will appear as a single blurred image and cannot be distinguished as separate entities.