How can I validate google recaptcha on the server side?

Question

I have a contact form and I'm trying to validate google's Recaptcha on the server-side. I'm using reCAPTCHA version 2. My HTML form looks like this:

<div class="container-contact100">
        <div class="wrap-contact100">
            <form class="contact100-form validate-form" action="form.php" method="POST">
                <span class="contact100-form-title">
                    Contact Us
                </span>

                <div class="wrap-input100 validate-input" data-validate="Name is required">
                    <input class="input100" type="text" name="name" placeholder="Full Name">
                    <span class="focus-input100-1"></span>
                    <span class="focus-input100-2"></span>
                </div>


                <div class="wrap-input100 validate-input" data-validate = "Valid email is required: [email protected]">
                    <input class="input100" type="text" name="email" placeholder="Email">
                    <span class="focus-input100-1"></span>
                    <span class="focus-input100-2"></span>
                </div>

                <div class="wrap-input100 validate-input" data-validate = "Message is required">
                    <textarea class="input100" name="message" placeholder="Tell us what kind of quote you're looking for"></textarea>
                    <span class="focus-input100-1"></span>
                    <span class="focus-input100-2"></span>
                </div>

                <!-- This is google's test sitekey.  -->
                <div class="g-recaptcha" data-sitekey="6LeIxAcTAAAAAJcZVRqyHh71UMIEGNQ_MXjiZKhI"></div>

                <div class="container-contact100-form-btn">
                    <button class="contact100-form-btn">
                        Submit
                    </button>
                </div>
            </form>
        </div>
    </div>

I've already validated this on the client side. But I'm trying to also validate this on the server side. I have PHP code that is attempting to validate it, which is:

<?php
        $captcha;
        echo '<script>alert("Welcome to Geeks for Geeks")</script>';
        if(isset($_POST['g-recaptcha-response'])){
          $captcha=$_POST['g-recaptcha-response'];
        }
        if(!$captcha){
          echo '<h2>Please check the the captcha form.</h2>';
          exit;
        }
        $secretKey = "6LeIxAcTAAAAAGG-vFI1TnRWxMZNFuojJ4WifJWe"; // This is google's test key for recaptcha
        $ip = $_SERVER['REMOTE_ADDR'];
        // post request to server
        $url = 'https://www.google.com/recaptcha/api/siteverify?secret=' . urlencode($secretKey) .  '&response=' . urlencode($captcha);
        $response = file_get_contents($url);
        $responseKeys = json_decode($response,true);
        // should return JSON with success as true
        if($responseKeys["success"]) {
                echo '<h2>Thanks for posting comment</h2>';
        } else {
                echo '<h2>You are spammer ! Get the @$%K out</h2>';
        }
?>

However, it doesn't seem to work. Whenever I submit the form, it just goes to a blank page. What am I doing wrong? How can I get it validated?