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A planoconvex lens is a type of lens with one flat (plane) surface and one outward-curving (convex) surface. This design is frequently used because it allows for efficient light focusing. Such lenses are often used in applications that require collimated light, like laser systems.
Here are some key points about planoconvex lenses:

• They converge light to a focal point, ideal for focusing applications.
• The flat side often faces the light source, minimizing spherical aberration.
• The curvature is involved in determining the lens's optical power.

Their function in optical systems is crucial. By bending incoming parallel light rays towards a focal point, planoconvex lenses can create real images. This property makes them valuable in any system that requires focused light.

The lensmaker's equation is an essential formula in geometric optics. It relates the focal length of a lens to the curvature of its surfaces and the refractive index of the material. This equation is expressed as:\[\frac{1}{f} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)\]where:

• \( f \) is the focal length of the lens.
• \( n \) is the refractive index of the lens material.
• \( R_1 \) and \( R_2 \) are the radii of curvature for the lens's two surfaces.

For planoconvex lenses, one radius is infinite because of the flat surface. This simplifies the equation, making calculations easier. The lensmaker's equation allows us to design and evaluate lenses based on desired focal properties. In the given exercise, you apply this formula to find the lens's focal length, which is crucial for determining image formation.

Image formation in lenses results from the bending of light rays as they pass through the lens. A planoconvex lens can form real images when positioned appropriately in relation to the object.

• Real images are produced on the opposite side of the lens from the object.
• They can be projected onto a screen because the light actually converges at a physical point.
• The equations used to determine the image distance include the lens formula: \( \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \) , where \(d_o\) is the object distance and \(d_i\) is the image distance.

In the problem, after employing the lensmaker's equation to find the focal length, the next step was to use this to calculate the image location. The resultant positive image distance indicated that the lens forms a real image, a common attribute of planoconvex lenses under typical orientations. This understanding is vital in various applications, such as imaging systems and optical instrumentation.

Magnification is a measure of how much larger or smaller the image is compared to the object itself. This concept is crucial for understanding how optics change the apparent size of objects.
The magnification \( m \) is given by:\[m = -\frac{d_i}{d_o}\]A positive magnification means the image is upright compared to the object, while a negative value indicates an inverted image. It also tells us the size ratio:

• If \(|m| > 1\), the image is larger than the object.
• If \(|m| < 1\), the image is smaller than the object.

In the exercise, after calculating the image location, the magnification formula was used to learn that the image is approximately 4.73 times larger than the original object. Additionally, due to the positive magnification value, the planoconvex lens produces an upright image. This concept is pivotal in many fields, including photography and microscopy, where image size and orientation are crucial parameters.