Optical Instruments – IIT‑JEE (Physics)
Goal of the chapter
Understand how refracting devices (lenses) are combined to build instruments that enlarge, magnify, or view distant objects.
Memorise the key formulae, know how to design a basic instrument, and be able to solve numerical problems.
1. Simple vs. Compound Instruments
| Feature | Simple | Compound |
|---|---|---|
| Uses | Single lens (or mirror) | Two or more lenses |
| Function | Magnify a single object | Combine large‑focal‑length objective with small‑focal‑length eyepiece |
| Field of View | Small | Larger |
| Example | Magnifying glass, simple telescope | Microscope, astronomical telescope, camera |
2. Fundamental Optical Relations
| Relation | Symbol | Description | Approximation (far‑field) |
|---|---|---|---|
| Lens formula | ( \displaystyle \frac{1}{f} = \frac{1}{v} - \frac{1}{u} ) | (f): focal length, (u): object distance, (v): image distance | |
| Linear magnification | ( m = -\frac{v}{u} ) | Magnification of the image (size & orientation) | |
| Angular magnification of a simple magnifier | ( M = \frac{1 + \frac{D}{f}}{1} ) | (D): near‑point (25 cm) | |
| Angular magnification of a telescope | ( M = \frac{f_o}{f_e} ) | (f_o): objective, (f_e): eyepiece | |
| Angular magnification of a microscope | ( M = \frac{L}{f_o}\cdot \frac{f_e}{l_e} ) | (L): tube length, (l_e): image distance in eyepiece (~f_e) | |
| Resolving power | ( \theta_{\min} = 1.22 \frac{\lambda}{D} ) | (D): diameter of objective | |
| Field of View (for telescope) | ( \text{FOV} \approx \frac{d_{\text{exit}}}{f_o} ) | (d_{\text{exit}}): exit pupil diameter |
Note: All distances are signed (positive for real, negative for virtual).
3. Optical Instruments
| Instrument | Basic Structure | Working Principle | Key Parameters |
|---|---|---|---|
| Magnifying Glass | Single convex lens | Object inside focal length → virtual, upright, enlarged image | Focal length (f); near‑point (D) |
| Microscope | Objective + tube + eyepiece | Objective forms real, enlarged, inverted image; eyepiece magnifies it | (f_o), (f_e), tube length (L), near‑point (D) |
| Astronomical Telescope | Objective + eyepiece | Objective forms a real, inverted image at its focal plane; eyepiece magnifies it | (f_o), (f_e), exit pupil, FOV |
| Terrestrial (Refractor) Telescope | Similar to astronomical but focused on near objects | Same as above but image is upright | |
| Binoculars | Two telescopes with prisms | Prisms reverse the image to correct orientation and allow both eyes to see | Prism type (roof/porro), exit pupil |
| Camera | Lens + film/CCD sensor | Lens projects image onto sensor; aperture controls light, depth of field | Focal length, aperture (f/#) |
| Eyepiece (Compound) | Single lens or a compound lens | Provides angular magnification of the intermediate image | (f_e) |
4. Design of a Simple Optical Instrument
4.1. Magnifying Glass
| Step | Calculation |
|---|---|
| Choose (f) (e.g., 10 cm) | |
| Angular magnification: ( M = 1 + \frac{D}{f} = 1 + \frac{25}{10} = 3.5 ) | |
| Image distance: ( v = \frac{f \cdot D}{D - f} ) (for near‑point) | ( v = \frac{10 \times 25}{25-10}=16.7) cm (virtual) |
| Verify: ( m = \frac{v}{u} \approx 3.5 ) |
5. Worked Example – Compound Microscope
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