The refractive index of the material of a concave lens is $\mu$. It is immersed in a medium of refractive index $\mu_{1.}$ A parallel beam of light is incident on the lens. The path of the emergent rays when $\mu_1>\mu$ is :

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Concepts Covered - 2

Thin lens

Thin lens-

Lens is a transparent medium bounded by two surfaces which refracts the light, such that at least one surface is curved. Curved surface can be cylindrical, spherical etc.

A thin lens is called convex if it is thicker at the middle as compare to the ends and it is called concave if it is thicker at the ends as compare to the middle. The figure shows the convex and concave lens -

There are few types of concave and convex lens as shown below -

From all the above shape we can see that there are two surfaces (may be spherical or plane), so there are two centres of curvature C₁ and C₂ and correspondingly two radii of curvature R₁ and R₂. In this case principal axis is the line joining C₁ and C₂ of the lens and the centre of the thin lens which is on the principal axis, is called the optical centre.

Now as there are two surfaces in the lens so there are two principal focus for the lens, which are :-

First principal focus(F₁) : An object point for which image is formed at infinity.

Second principal focus(F₂) : An image point for an object at infinity.

Note -

1. In this chapter we are mainly concerned with the second principal focus (F₂). So, whenever or wherever we use the term focus, it means the second principal focus.

2. A ray passing through optical centre proceeds undeviated through the lens.

SIgn convention in lens - All the distances along the direction of the incident light ray is positive if we measure the distances from the pole of the lens. Also all the distances above the principle axis is taken as positive and below the principle axis is taken as negative. All these convention can be seen from the figure given below -

Image result for sign convention in lens

Image formation by lens

Image formation by lens-

In this concept we will discuss how and where the image will form with different position of object in concave and convex lens. Let us discuss both the lens one by one -

Convex lens -

The figure given below shows the position of image formation for different position of the object -

So, from this image we can conclude the floolwing table -

For convex lens -

Object location	Image location	Image nature	Image size
Infinity	At F	Real and Inverted	Diminished
Beyond 2F	Between 2F and F	Real and Inverted	Diminished
Between 2Fand F	Beyond 2F	Real and Inverted	Enlarged
At F	At infinity	Real and Inverted	Enlarged
At 2F	At 2F	Real and Inverted	Same size
Between Fand 0	On the same side as object	Virtual and Erect	Enlarged

For concave lens -

Object location	Image location	Image nature	Image size
Infinity	At F	Virtual and Erect	Highly Diminished
Beyond infinity and 0	Between F and Optical centre	Virtual and Erect	Diminished