Light Lab
Drag the object, watch the rays, and check the sign convention.
1/v = 1/f − 1/u = 1/(−15.0) − 1/(−40.0) = −0.0417, so v = −24.0 cm. m = minus v over u = −0.60.
New Cartesian sign convention: distances are measured from the pole P. Along the incident light (left to right) is positive, against it is negative; heights above the axis are positive.
With the object beyond C, the reflected rays meet between F and C, giving a real, inverted and diminished image in front of the mirror. Slide the object towards C and watch the image grow and move outwards.
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NCERT Class 10 · Class 12
Everything the simulator uses, in the form you will write it in the board exam.
With this convention the focal length of a concave mirror and of a concave lens is negative, and that of a convex mirror and of a convex lens is positive. For a spherical mirror, f = R/2, where R is the radius of curvature.
1/v + 1/u = 1/f
m = h′/h = −v/u
Used for concave and convex mirrors. A real image forms in front of the mirror (v negative); a virtual image forms behind it (v positive).
1/v − 1/u = 1/f
m = h′/h = v/u
Used for convex and concave lenses. A real image forms on the other side of the lens (v positive); a virtual image forms on the same side as the object (v negative).
m is negative
The image is real and inverted.
m is positive
The image is virtual and erect.
Size of |m|
Greater than 1: magnified. Equal to 1: same size. Less than 1: diminished.
The two follow the same pattern: C of the mirror plays the part of 2F of the lens. Try each row in the lab above with the object-position presets.
| Position of the object | Image: concave mirror | Image: convex lens | Nature | Size |
|---|---|---|---|---|
| At infinity | At F | At F₂ | Real, inverted | Highly diminished, point-sized |
| Beyond C (beyond 2F₁) | Between F and C | Between F₂ and 2F₂ | Real, inverted | Diminished |
| At C (at 2F₁) | At C | At 2F₂ | Real, inverted | Same size |
| Between C and F (between 2F₁ and F₁) | Beyond C | Beyond 2F₂ | Real, inverted | Enlarged |
| At F (at F₁) | At infinity | At infinity | Real, inverted | Highly enlarged |
| Between F and P (between F₁ and O) | Behind the mirror | On the same side as the object | Virtual, erect | Enlarged |
A convex mirror and a concave lens always form a virtual, erect and diminished image: behind the convex mirror between P and F, and between F₁ and O on the object side of the concave lens. For an object at infinity, that image is point-sized and sits at F.
An object is placed 30 cm in front of a concave mirror of focal length 20 cm. Here u = −30 cm and f = −20 cm. Then 1/v = 1/f − 1/u = −1/20 + 1/30 = −1/60, so v = −60 cm. The magnification is m = −v/u = −(−60)/(−30) = −2. The image is real, inverted, twice the size of the object and 60 cm in front of the mirror, beyond C.
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