Physics — Ray Path Through a Two-Lens System
Compound microscope ray path: the objective forms a real inverted image inside the eyepiece's focal length, and the eyepiece works as a magnifier to give a virtual final image at the near point.
Rendering…
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{
"nodes": [
{
"id": "op-ray1",
"type": "note",
"label": "Ray 1 — leaves the object parallel to the principal axis and is refracted through the far focal point F′.",
"x": 60,
"y": 60,
"width": 240,
"height": 117,
"fill": "#fef9c3",
"stroke": "#ca8a04"
},
{
"id": "op-ray2",
"type": "note",
"label": "Ray 2 — passes through the optical centre of the lens and continues undeviated. The quickest ray to draw.",
"x": 340,
"y": 60,
"width": 240,
"height": 117,
"fill": "#fef9c3",
"stroke": "#ca8a04"
},
{
"id": "op-ray3",
"type": "note",
"label": "Ray 3 — passes through the near focal point F and emerges parallel to the axis. Any two of the three fix the image.",
"x": 620,
"y": 60,
"width": 240,
"height": 117,
"fill": "#fef9c3",
"stroke": "#ca8a04"
},
{
"id": "op-obj",
"type": "icon",
"label": "Object h = 0.10 mm · placed just outside f₀",
"x": 60,
"y": 235,
"width": 240,
"height": 117,
"fill": "#e0f2fe",
"stroke": "#0369a1",
"iconId": "mdi:arrow-up-bold"
},
{
"id": "op-objective",
"type": "ellipse",
"label": "Objective lens f₀ = 8.0 mm (biconvex, converging)",
"x": 340,
"y": 235,
"width": 240,
"height": 117,
"fill": "#ede9fe",
"stroke": "#6d28d9"
},
{
"id": "op-inter",
"type": "icon",
"label": "Intermediate image — real, inverted, magnified ×19",
"x": 620,
"y": 235,
"width": 240,
"height": 117,
"fill": "#fce7f3",
"stroke": "#be185d",
"iconId": "mdi:arrow-down-bold"
},
{
"id": "op-eyepiece",
"type": "ellipse",
"label": "Eyepiece fₑ = 25 mm (converging, used as a magnifier)",
"x": 900,
"y": 235,
"width": 240,
"height": 117,
"fill": "#ede9fe",
"stroke": "#6d28d9"
},
{
"id": "op-eye",
"type": "ellipse",
"label": "Relaxed eye at the eye-point",
"x": 1180,
"y": 235,
"width": 240,
"height": 117,
"fill": "#e0f2fe",
"stroke": "#0369a1"
},
{
"id": "op-u",
"type": "note",
"label": "Object distance u = 8.4 mm — only 0.4 mm outside f₀ = 8.0 mm. Move it inside f₀ and no real image forms at all.",
"x": 60,
"y": 410,
"width": 240,
"height": 117,
"fill": "#fef9c3",
"stroke": "#ca8a04"
},
{
"id": "op-v",
"type": "note",
"label": "1/u + 1/v = 1/f with v = 160 mm (the tube length) gives u = 8.42 mm and linear magnification m₀ = v/u = 19×.",
"x": 340,
"y": 410,
"width": 240,
"height": 117,
"fill": "#fef9c3",
"stroke": "#ca8a04"
},
{
"id": "op-inside",
"type": "note",
"label": "The intermediate image lands just INSIDE fₑ = 25 mm of the eyepiece. That is the condition for the eyepiece to act as a simple magnifier.",
"x": 620,
"y": 410,
"width": 240,
"height": 117,
"fill": "#fef9c3",
"stroke": "#ca8a04"
},
{
"id": "op-me",
"type": "note",
"label": "Eyepiece angular magnification Mₑ = D/fₑ = 250/25 = 10×, taking the near point D as 250 mm.",
"x": 900,
"y": 410,
"width": 240,
"height": 117,
"fill": "#fef9c3",
"stroke": "#ca8a04"
},
{
"id": "op-total",
"type": "note",
"label": "Total magnification M = m₀ × Mₑ ≈ 19 × 10 ≈ 190×. The barrel markings ×20 and ×10 use the L/f₀ approximation.",
"x": 1180,
"y": 410,
"width": 240,
"height": 117,
"fill": "#fef9c3",
"stroke": "#ca8a04"
},
{
"id": "op-virtual",
"type": "note",
"label": "A virtual image cannot be caught on a screen: the rays only appear to diverge from it. Draw the back-projection dashed.",
"x": 60,
"y": 585,
"width": 240,
"height": 117,
"fill": "#fef9c3",
"stroke": "#ca8a04"
},
{
"id": "op-final",
"type": "icon",
"label": "Final virtual image — inverted, 250 mm from the eye",
"x": 620,
"y": 585,
"width": 240,
"height": 117,
"fill": "#fce7f3",
"stroke": "#be185d",
"iconId": "mdi:arrow-down-bold"
},
{
"id": "op-limit",
"type": "note",
"label": "Resolution, not magnification, is the real limit: d = λ/(2 NA) ≈ 0.2 µm at λ = 550 nm and NA = 1.4. Beyond that you get empty magnification.",
"x": 1180,
"y": 585,
"width": 240,
"height": 117,
"fill": "#fef9c3",
"stroke": "#ca8a04"
}
],
"edges": [
{
"id": "op-e1",
"source": "op-obj",
"target": "op-objective",
"label": "diverging cone of rays"
},
{
"id": "op-e2",
"source": "op-objective",
"target": "op-inter",
"label": "converge to a real image at v = 160 mm"
},
{
"id": "op-e3",
"source": "op-inter",
"target": "op-eyepiece",
"label": "acts as the object for the eyepiece"
},
{
"id": "op-e4",
"source": "op-eyepiece",
"target": "op-eye",
"label": "parallel bundle into a relaxed eye"
},
{
"id": "op-e5",
"source": "op-eyepiece",
"target": "op-final",
"label": "rays traced back — virtual image",
"style": "dashed"
}
]
}