1. Give the image formation due to convex lens at a glance at different positions. Also give the nature and size of the images formed and some applications of the convex lens. 

Convex Lens Examples: The simplest example is the magnifying glass. The letters which are too small to read can easily be read by using a convex lens as a magnifying glass. The lens is held in such a way that the letters are within the focal length of the lens. Hence the letters are magnified and in upright position to make it easy to read. The same principle is used in spectacles which are used in correction of hyperopia. In olden days convex lens are used to ignite by allowing the sun rays to be focused on the object to be ignited. Here the lens converge the heat rays just like converging the light rays.

2. How is the refraction by a concave lens? Explain with the help of diagram.

 The above diagram shows, just like the convex lens, two incident rays approaching parallel to the principal axis of the double concave lens, light bends towards the normal when entering and away from the normal when exiting the lens. These incident rays are not converged to a point upon refraction through the lens, rather, diverge upon refracting through the lens. For this reason, a double concave lens can never produce a real image, which produces virtual images. If the refracted rays are extended backwards behind the lens, the refracted rays will intersect at a point. This point is known as the focal point. Since a concave lens does not really focus the incident light rays, rather, it diverges these light rays, a concave lens is said to have a negative focal length. The refracted ray extended backwards and the ray coming directly from the object and passes through the optic centre of the lens, meet at a point where the virtual image is formed. The formation of the image by a concave lens is shown below.

The focal length of the concave lens can be calculated using the formula,

                            1/f = 1/u + 1/v

where f is the focal length, u is the object distance and v is the image distance and v is negative with respect to u.

3. What are the differences in refraction between concave lens and convex lens?

A convex lens makes objects look farther away. A convex lens refracts light rays inward. If a convex lens is held close to a person’s eyes, they will see an image that is upright and larger than the actual object. All the rays meet at F. This is the reason why a convex lens is called a converging lens.

A convex lens focuses light rays coming from infinite distance at its focal point. 

Concave lens makes objects look smaller and closer and correct nearsightedness. A concave lens refracts light rays spreading them outward producing an image that is upright and smaller than the actual object. The incident ray passes un-deviated along the principal axis. All the rays appear to meet at F behind the concave lens. This is the reason why a concave lens is called a diverging lens.

A concave lens defocuses light rays coming from infinite distance. The parallel light rays appear to diverge from the focal point of the lens.

Refraction Rules for a converging lens:

• Any incident ray traveling parallel to the principal axis of a converging lens will refract through the lens and travel through the focal point on the opposite side of the lens.
• Any incident ray traveling through the focal point on the way to the lens will refract through the lens and travel parallel to the principal axis.
• An incident ray that passes through the center of the lens will in affect continue in the same direction that it had when it entered the lens.

Refraction Rules for a diverging lens:

• Any incident ray traveling parallel to the principal axis of a diverging lens will refract through the lens and travel in line with the focal point (i.e., in a direction such that its extension will pass through the focal point).
• Any incident ray traveling towards the focal point on the way to the lens will refract through the lens and travel parallel to the principal axis.
• An incident ray that passes through the center of the lens will in affect continue in the same direction that it had when it entered the lens.

4. Compare and contrast camera and human eye. 

  The functions of camera and human eye are alike. Both contain a convex lens with adjustment facility, a screen for catching the image and a light proof apartment which encloses the lens and the screen.

  In the camera there is a convex lens which is fixed to a box with adjustment facility. There is a screen which has a photo sensitive film. The shutter permits light to enter the camera as it is opened. An object is placed in front of the camera, focused in such a way that the image is formed on the film by adjusting the position of the lens. The shutter is opened to receive the light from the object for few seconds and closed. The light reacts with the film and forms an image inverted. The film in the camera is removed and further processed to get prints, called photos. The modern cameras are more sophisticated and their mechanisms are complicated. Video cameras work with reusable films in the form of tapes. Cameras which do not require films and tapes are used in satellites. 

  The function of the eye is similar to that of the camera. Eye lids behave as the shutters like the cameras. The eye lens is also convex in nature which helps in focusing images. The screen and the film in the human eye is called retina on which image is formed and the corresponding signals are processed through our brain. The eye-ball behaves as a light proof compartment. The eye contains a self-adjusting aperture, an automatic focus system, and inner surfaces surrounded by a dark pigment to minimize the scattering of stray light. Sensitivity range of the eye gives us excellent vision in bright sunlight as well as in the dimmest moonlight. Its color-analysis system enables the eye to distinguish millions of shades of color and quickly just to the lighting conditions. The eye-brain combination produces depth perception that is beyond the range of any camera. Light passes through the cornea, which has the greatest effect on focus. It is the cornea that determines whether someone is nearsighted, or has astigmatism. This is the part of the eye corrected by Lasik surgery.

5. What are the problems of vision? How are they rectified? 

The inability of eye lens to adjust itself gives rise to problems of vision. The problems of vision are of two types. These two vision problems stem from the eye not being able to focus light exactly on the retina. They are

(i) Myopia (ii) Hypermetropia or Hyperopia.

    Hyperopia, also known as farsightedness, longsightedness or hypermetropia, is a defect of vision caused by an imperfection in the eye (often when the eyeball is too short or the lens cannot become round enough), causing difficulty focusing on near objects. If the power of the cornea and lens is insufficient, as in hyperopia, the image will appear blurred. Hypermetropia is characterised by a slight shortening of the eyeball, causing the image to fall a little behind the retina.

   As an object moves toward the eye, the eye must increase its optical power to keep the image in focus on the retina. By placing a convex (plus powered) lens in front of a hypermetropic eye, the image is moved forward and focuses correctly on the retina.

Myopia is commonly known as nearsightedness and shortsightedness. Myopia is a condition of the eye where the light that comes in does not directly focus on the retina but in front of it. This causes the image that one sees when looking at a distant object to be out of focus but in focus when looking at a close object. Myopia is characterized by the elongated eyeball causing the image to fall in front of the retina.

Eye care professionals most commonly correct myopia through the use of corrective lenses, such as concave lenses or contact lenses. It may also be corrected by refractive surgery, though there are cases of associated side effects. The corrective lenses have a negative optical power, i.e concave lens, which compensates for the excessive positive diopters of the myopic eye.

6.  An object is placed at a distance of 50 cm from a concave lens of focal length 20 cm. Find the nature and position of the image.

The distance between the object and the lens (u) = -50 cm
Focal length f = -20 cm
Distance of the image from the optic centre = v

The image is formed at a distance of 14.3 cm from the lens on the same side as the object and since v is negative the image formed is virtual and erect.

7. What are the differences between a microscope and a telescope? 

    Telescope and Microscope are two scientific instruments that serve their purposes differently.

1) One of the main differences between a telescope and a microscope is that a telescope is used to view things that are far whereas a microscope is used to view things that are very near.

2) A microscope makes a tiny, nearby object look much bigger. A telescope makes a large, distant object or scene appear much closer and brighter.

3) Another important difference between telescope and microscope is that the objective of a compound microscope is a convex lens of very short focal length (f₀ ) that is ˂ 1cm whereas the objective lens of telescope is a convex lens of long focal length. 

4) A microscope is used to look into smaller details like the structure of the cells and the unicellular organism. Telescope is an instrument helps in seeing heavenly bodies like the moon, planet and stars.

5) The objective lens of a microscope is designed to produce a real image of something that is close to the lens, and the real image will be larger than the object you are looking at. The objective lens of a telescope is designed to produce a real image of something that is at a much larger distance, and the real image will usually be smaller than the object (usually much, much smaller!). The longer the focal length of the objective, the larger the real image will be.

8.  Write the principle and working of a compound microscope. 

     A compound microscope is an optical instrument which is used to magnify very small objects like blood cells, bacteria which otherwise cannot be seen with the naked eye.

Principle: Compound microscope has two sets of lenses, the objective and the eyepiece. The basic principle behind it is to visualize the enlarged image of the object by the help of these lenses. When the beam of light passes through the object and then convex lens of objective, it forms a real inverted and enlarged image of the object in the focal plane of eyepiece (by adjustment). This image now acts as object for the eyepiece. Eyepiece finally forms a further enlarged virtual image of the object. Thus, magnifying power of a compound microscope is the multiplication product of magnifying powers of objective and eyepiece.

 The essential parts of a compound microscope are two convex lenses of short focal length. These lenses are referred to as:

a) objective lens or objective: The objective lens of a compound microscope is a convex lens of very short focal length (f₀ ) that is ˂ 1cm. The object is kept very close to the objective lens.

b) eye piece: The eye piece of compound microscope is also a convex lens of short focal length (fe). But fe ˃ fo. 

c) Microscope tube: The objective lens and the eye piece are mounted coaxially at the ends of two bras tubes which can be made to slide into each other so that the distance between the lenses can be adjusted.

     Working of Compound Microscope

    The ray diagram given below gives the principle of a compound microscope. The object O is mounted on the stand below the microscope tube. The objective lens forms a real, inverted and magnified image (I₁) of the object. The image I₁ acts as an object for the eye piece. The position of the eyepiece is so adjusted that the image lies within the focus of the eyepiece (F_e). The eyepiece acts like a magnifying glass and forms a virtual erect and magnified image of the object I₂.

Image Formation in a Compound Microscope.

• The object (O) is placed just outside F_o, the principal focus of the objective lens.
• F_e is the principal focus of the eye lens.
• A real, inverted magnified image I₁ is formed. The magnified image I₁ acts as an object for the eye lens.
• The final image I₂ is virtual and is magnified still further. It is inverted compared with the object. I₂ may appear 1000 times larger than the object.

9. Write the principle and working of a Astronomical telescope.

A Telescope is an instrument used for viewing objects at very large distances. Astronomical Telescopes are used to look at objects in the sky such as the moon and other celestial objects. This telescope is an amazing device that has the ability to make faraway objects appear much closer and is used in Astronomy. Basically it is a device for practical observation of sky, planets, moon and stars.

   Principle of Operation: A Telescope is constructed using an objective that gathers light from a faraway source and an eye-piece that forms an image that the eye can see. The objective gathers the light from the object to be viewed and focuses it on a point. The second lens the eye-piece collects the light from the focal point of the objective and enlarges it. The magnifying power and the resolution of the telescope are dependent on the choice of the lenses.

Structure of Astronomical Telescope

Astronomical telescope mainly consists of two convex lenses that are placed in a coaxial manner. The lens that is located closer to the eye is called an eyepiece. The lens that is placed farther away is called an objective lens. The focal length of the eye piece is always smaller than the objective lens.

Working of Astronomical Telescope.

Once the telescope gets focused on a far away object, like a star, the parallel rays that comes from the star forms a small image, P¹Q¹,that is real and inverted. It is the image that acts as an object for the eyepiece. The eyepiece can be moved back and forth to generate a virtual image of P¹Q¹ called P¹¹Q¹¹. This image is magnified. The final image version of P¹¹Q¹¹ that is formed is upside down when compared to the object. Hence, the farther away objects are observed as a magnified image.