Week 7

Other Notes

Sign convention

The sign convention for lenses is similar to that for mirrors. Again, take the side of the lens where the object is to be the positive side. Because a lens transmits light rather than reflecting it like a mirror does, the other side of the lens is the positive side for images. In other words, if the image is on the far side of the lens as the object, the image distance is positive and the image is real. If the image and object are on the same side of the lens, the image distance is negative and the image is virtual.

For converging mirrors, the focal length is positive. Similarly, a converging lens always has a positive f, and a diverging lens has a negative f.

The signs associated with magnification also work the same way for lenses and mirrors. A positive magnification corresponds to an upright image, while a negative magnification corresponds to an inverted image. As usual, upright and inverted are taken relative to the orientation of the object.

Note that in certain cases involving more than one lens the object distance can be negative. This occurs when the image from the first lens lies on the far side of the second lens; that image is the object for the second lens, and is called a virtual object.

converging lens: a convex lens in which light rays that enter it parallel to its axis converge at a single point on the opposite side

diverging lens: a concave lens in which light rays that enter it parallel to its axis bend away (diverge) from its axis

focal point: for a converging lens or mirror, the point at which converging light rays cross; for a diverging lens or mirror, the point from which diverging light rays appear to originate

focal length: distance from the center of a lens or curved mirror to its focal point

magnification: ratio of image height to object height

power: inverse of focal length

real image: image that can be projected

virtual image: image that cannot be projected

Convex Lens Rules

Rule 1: A ray of light which is originally parallel to the principal axis passes through the focus after refraction through the lens.

Rule 2: A ray of light passing through the optical centre of the convex lens does not bent after refraction but goes straight. Also, a ray of light going along the path of principal axis of a convex lens also goes straight and does not deviate.

Rule 3: When a ray of light passes through the focus of the convex lens then it becomes parallel to the principal axis after refraction through the lens.

Convex Formation of Images

Case 1: If the object is placed between optical centre and focus (between C and F’) then the first ray of light starting from the top of the object is parallel to the principal axis. Therefore, as per the rule, it passes through another focus after refraction through the lens. Another ray of light from the object passes through the optical centre of the lens and thus as per the rule goes straight after refraction through the lens. Thus, both the light rays diverge after refraction through the lens and does not meet. Therefore, both the refracted rays are produced backwards so that they meet at a point to form an image.

The image formed will be: Behind the object, virtual and erect and larger than the object.

Case 2: When the object is placed at the focus of the convex lens (at F’) then it means that the object is placed at the distance equal to the focal length of the lens.

One ray of light becomes parallel to the principal axis of the lens and thus, passes through another focus after refraction through the lens. Another ray of light passes through the optical centre of the lens and goes straight.

Therefore, the image formed is: At infinity, Real and inverted, highly enlarged.

Case 3: When the image is placed between focus and distance less than twice the focal length (F’ and 2F’) then a ray of light parallel to the principal axis of the lens passes through another focus (F) after refraction through the lens. Another ray of light passes through optical centre of the lens and goes straight.

Therefore, the image formed is: Real and inverted, Larger than object and beyond 2F.

Case 4: When the object is paced at the distance equal to twice the focal length ( at 2F’) of the convex lens then one ray of light becomes parallel to the principal axis and passes through another focus of the lens after refraction. Another ray of light passes though optical centre and goes straight after refraction. Both the refracted light rays meet at 2F` on another side.

The image formed is: Real and inverted, same size as that of an object.

Case 5: When the object is placed at the distance greater than twice the focus (beyond 2F’) one ray of light becomes parallel to principal axis and passes through focus after refraction through the lens and another light ray passes through optical centre and goes straight after refraction.

The image formed is: Between F and 2F, Real and inverted, Smaller than object.

Case 6: When the object is placed at infinity, the light rays become parallel after reaching the lens.

Concave Lens Rules

Rule 1: A ray of light parallel to the principal axis of the concave lens appears to be coming from focus after refraction through the lens.

Rule 2: A ray of light passing through the optical centre of the concave lens goes straight after refraction through the lens.

Rule 3: A ray of light going towards the focus on another side of the concave lens becomes parallel to the principal axis after refraction through the lens.

Concave Formation of Images

Case 1: When an object is placed anywhere between optical centre and infinity, the image formed is between optical centre and focus.

Case 2: When an object is placed at infinity, the image formed by concave lens will be at focus.