Object at F₁ or inside F₁

The idea

For a convex lens, an object at F1 forms its image at infinity, while an object between F1 and the optical centre gives a virtual, erect, enlarged image on the same side of the lens as the object.

Moving the object in

A convex lens makes a real image of an object that is far from it. Now an object is brought closer and closer to the lens, until it is nearer than the focus F₁.

What do you think happens to the image when the object is inside F₁?

• The image appears on the same side of the lens as the object
• The image is still real on the other side
• The image disappears for ever

Slide the object

Red ray: parallel to the axis. Purple ray: through the optical centre. Slide the object to F₁, and then to a place between F₁ and the lens.

Two special places

At F₁ the refracted rays went out parallel and never met. Inside F₁ they spread out, and their dashed extensions met on the same side as the object.

For a convex lens, an object at F₁ forms its image at infinity (no image is formed), while an object between F₁ and the optical centre gives a virtual, erect, enlarged image on the same side of the lens as the object.

Notes

A convex lens gives no image for an object at F₁ (it would be at infinity) and a virtual, erect, enlarged image on the same side as the object for an object between F₁ and O.

Check yourself

An object is placed at F₁ of a convex lens. What happens to the refracted rays?

An object is between F₁ and the optical centre of a convex lens. The image is

Where is the virtual image of an object between F₁ and O of a convex lens?

For which position of the object does a convex lens give a virtual image?

• They meet at 2F₂ and form a same-size image. A same-size image at 2F₂ is formed for an object at 2F₁.
• They meet at F₂ and form a point-sized image. A point-sized image at F₂ is formed for an object at infinity.
• They go out parallel to each other, so no image is formed — correct. Yes!
• virtual, erect and enlarged — correct. Yes!
• real, inverted and enlarged. That image is for an object between F₁ and 2F₁.
• virtual, erect and diminished. A convex lens enlarges an object that is between F₁ and O. A diminished virtual image is what a concave lens gives.
• On the other side of the lens. Real images are formed on the other side. This virtual image is on the same side as the object.
• On the same side of the lens as the object — correct. Yes!
• At F₂. An image at F₂ is formed by an object at infinity.
• Between F₁ and 2F₁. An object between F₁ and 2F₁ gives a real image beyond 2F₂.
• At 2F₁. An object at 2F₁ gives a real image of the same size at 2F₂.
• Between F₁ and the optical centre — correct. Yes!