Question

The above image is that of a Digital Single Lense Reflector (DSLR) Camera which are used to take high resolution photographs by professional photographers. The second image of the above two is a schematic diagram of how an image is formed on the sensor of the camera. Based on your understanding of the lenses, answer the following questions.

1. What type of lens is used in the DSLR camera shown in the image?
2. What type of image is formed on the sensor?
3. A photographer is using a DSLR camera with a lens of focal length f = 50 mm to take a close-up photograph of a small object. The lens projects an image onto the camera sensor that is located 60 mm behind the lens. Calculate the object distance (i.e., the distance between the object and the lens).
   OR
4. A photographer is using a DSLR camera to take a picture of a flower. The flower is positioned 150 mm away from the camera lens. The actual height of the flower is 80 mm, and the image height formed on the camera’s sensor is measured to be 20 mm. Calculate the focal length of the camera lens.

Answer 1

A. A convex lens is used in DSLR camera to converge light rays and form real images on the sensor.

B. Convex lens forms a real and inverted image when the object is placed beyond the focal point.

C. Given, Focal length of lens (F) = 50 mm

Image distance (v) = 60 mm

Object distance, u = ?

Using lens formula,

`1/f = 1/v - 1/u`

⇒ `1/u = 1/v - 1/f`

= `1/60 - 1/50`

= `(50 - 60)/3000`

= `(-1)/300`

⇒ u = −300 mm

∴ The object distance is 300 mm in front of the lens (the negative sign indicates the object is on the opposite side of the image).

OR

D. Given, Object distance (u) = −150 mm

Object height (h₀) = 80 mm

Image height (h₁) = −20 mm (inverted image)

m = `h_1/h_0`

= `(-20)/80`

= −0.25 mm

Now, m = `v/u`

⇒ v = m × u

= (−0.25) × (−150)

= 37.5 mm

Using magnification formula,

`1/f = 1/v - 1/u`

= `1/37.5 - 1/-150`

= `1/37.5 + 1/150`

= `(1 xx 4)/(37.5 xx 4) + 1/150`

= `4/150 + 1/150`

= `(4 + 1)/150`

= `5/150`

`1/f = 1/30`

f = 30 mm

Hence, the focal length of the camera lens is 30 mm.