What is meant by power of a lens? What does it's sign (positive or negative) indicate? State its SI unit. How is it related to the focal length of a lens?

To find the image for varying object distances in case of a convex lens, a student obtains on a screen a sharp image of a bright object placed very far from the lens. After that he gradually moves the object towards the lens and each time focuses its image on the screen.

(a) In which direction-towards or away from the lens does he moves the screen to focus the object?

(b) What happens to the size of image-does it increase or decrease?

(c) What happens when he moves the object very close to the lens?

A concave lens made of a material of refractive index $n_1$ is kept in medium of refractive index $n_2$. A parallel beam light is incident on the lens. Complete the path of rays of light emerging from the concave lens if
  $$\begin{gathered} \left(i\right) n_1>n_2 \\ \left(ii\right) n_1=n_2 \\ \left(iii\right) n_1<n_2 \end{gathered}$$

(a) Two lenses have power of (i) $2\mathrm{D}$ (ii) $-4\mathrm{D}$. What is the nature of focal length of each lens?

(b) An object is kept at a distance of $100 \mathrm{cm}$ from each of the above lenses. Calculate  (i) image distance  (ii) magnification in each of two cases.

One half of a convex lens of focal length $10 \mathrm{cm}$ is covered with a black paper. Can such a lens produce an image of a complete object placed at a distance of $30 \mathrm{cm}$ from the lens? Draw a ray diagram to justify your answer.

A $4 \mathrm{cm}$ tall object is placed perpendicular to the principal axis of a convex lens of focal length $20 \mathrm{cm}$. The distance of the object from the lens is $15 \mathrm{cm}$. Find the nature, position and size of the image. 

Analyse the following observations table showing variation of image distance ($v$) with object distance ($u$) in case of a convex lens and answer the questions that follow, without doing any calculations:

 (a) What is the focal length of the convex lens? Give reason in support of your answer. 

(b) Write the serial number of that observation which is not correct. How did you arrive at this conclusion?

(c) Take an appropriate scale to draw ray diagram for the observation at S.No.$4$ and find the approximate value of magnification.

Which of the following can make a parallel beam of light when light from a point source is incident on it?

A $10 \mathrm{mm}$ long awl pin is placed vertically in front of a concave mirror. A $5 \mathrm{mm}$ long image of the awl pin is formed at $30 \mathrm{cm}$ in front of the mirror. The focal length of this mirror is