Animated Solution for Physics - Optics: A real image of a distant object is formed by a plano-convex lens on its principal axis. Spherical aberration

Have you ever looked through a cheap magnifying glass and noticed that the edges of the image look blurry or distorted, even when the center is perfectly sharp? This annoying optical flaw is known as spherical aberration.

It occurs because a lens with spherical surfaces cannot bring all incoming light rays to a single, perfect focal point. The rays passing near the edges of the lens (marginal rays) are bent more sharply than the rays passing near the center (paraxial rays). As a result, the marginal rays focus closer to the lens, creating a "blur circle" instead of a sharp point.

Sharing the Load

So, how do optical engineers minimize this effect without resorting to expensive, complex aspheric lenses? The secret lies in a simple principle: Spherical aberration is minimized when the total deviation of a light ray is equally divided between the two refracting surfaces of the lens.

Think of it like carrying a heavy load. If one person carries the entire weight, they will struggle and stumble. But if two people share the load equally, the journey is much smoother. In optics, if one surface of the lens does all the bending, the aberration is severe. If both surfaces share the bending, the aberration is minimized.

Let's apply this to a plano-convex lens—a lens with one flat (plane) surface and one curved (convex) surface. Suppose we are trying to focus light from a distant object, like a star or the sun. The light rays arriving from a distant object are essentially parallel.

Scenario 1: Plane Surface Facing the Object If the parallel rays hit the flat surface first, they strike it at a $90^{\circ }$ angle (along the normal). According to Snell's Law, they pass straight through without bending at all! This means the flat surface does zero work. When the rays reach the second, convex surface, it has to do 100% of the bending to focus the light. This unequal sharing leads to massive spherical aberration.

Scenario 2: Curved Surface Facing the Object Now, let's flip the lens. The parallel rays hit the convex surface first. Because the surface is curved, the rays strike it at an angle and bend towards the normal. Then, they travel through the glass and hit the flat surface from the inside. As they exit into the air, they bend away from the normal.

In this orientation, the first surface does some bending, and the second surface does the rest. The total deviation is beautifully shared between the two surfaces.

Because the deviation is shared when the curved surface faces the incoming parallel rays, the spherical aberration is significantly reduced. Therefore, to get the sharpest possible real image of a distant object using a plano-convex lens, the curved surface must face the object.

Interestingly, if you were using the lens to focus light from a very near object (like a tiny LED bulb placed close to the lens), the diverging rays would require the opposite orientation—the plane surface should face the object—to achieve that perfect sharing of deviation!